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0 0 0 1 }{CSTYLE "" -1 322 "" 1 12 0 0 56 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 323 "" 1 14 0 0 56 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 324 "" 1 12 0 0 56 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 325 "" 1 12 0 0 56 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 326 "" 1 12 0 0 56 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE " " -1 327 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 328 "" 1 12 0 0 56 0 0 1 0 0 0 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 2" -1 4 1 {CSTYLE "" -1 -1 "Times" 1 14 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 4 4 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Out put" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 4 "" 0 "" {TEXT 260 14 "Ejercicios de " }}{PARA 4 "" 0 "" {TEXT 261 46 "(5) Sistemas aut\363nomos: m\351todos de RUNGE -KUTTA" }}{PARA 4 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT 259 15 "Ejercicio 05-02" }}{PARA 4 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 " " {TEXT -1 40 "Para el problema tipo aut\363nomo de Cauchy" }}{PARA 4 "" 0 "" {TEXT -1 14 " y'_1 = " }{XPPEDIT 18 0 "(-y_1^2+y_2^4)/y_ 2^2" "6#*&,&*$%$y_1G\"\"#!\"\"*$%$y_2G\"\"%\"\"\"F,*$F*F'F(" }{TEXT -1 4 " " }}{PARA 4 "" 0 "" {TEXT -1 15 " y'_2 = " }{XPPEDIT 18 0 "-y_1/y_2" "6#,$*&%$y_1G\"\"\"%$y_2G!\"\"F(" }{TEXT -1 6 " \+ " }}{PARA 4 "" 0 "" {TEXT -1 28 " y_1(0) = 0 , y_2(0) = 1" }} {PARA 4 "" 0 "" {TEXT -1 88 "(de soluci\363n exacta y_1(x) = sen(x) \+ cos(x) , y_2(x) = cos(x) ) util\355cese el m\351todo de " }}{PARA 4 " " 0 "" {TEXT -1 18 "TAYLOR de orden 3 " }{TEXT 256 73 "para aproximar \+ la soluci\363n en x = 0.3 tomando amplitud de paso h = 0.1" }} {PARA 4 "" 0 "" {TEXT 262 2 "Re" }{TEXT -1 63 "al\355cense las operaci ones con 3 cifras significativas y redondeo" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "interface(labeling=false):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "Digits:=3:" }}}{EXCHG {PARA 4 "" 0 "" {TEXT 257 41 "El sistema (aut.) y la verdadera soluci\363n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "f[1]:=unapply((-y1^2+y2^4)/y2^2,y1,y2):\nf[2]:=unappl y(-y1/y2,y1,y2):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "yv[1]:= unapply(sin(x)*cos(x),x):\nyv[2]:=unapply(cos(x),x):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 258 37 "Los m\351todos de TAYLOR y el de orden 3" }}} {EXCHG {PARA 4 "" 0 "" {TEXT 263 64 "Los m\351todos de TAYLOR para sis temas aut\363nomos y en los primeros " }}{PARA 4 "" 0 "" {TEXT 320 34 "\363rdenes se escriben vectorialmente" }}{PARA 4 "" 0 "" {TEXT 264 4 " " }{XPPEDIT 18 0 "y[n+1]" "6#&%\"yG6#,&%\"nG\"\"\"F(F(" }{TEXT 265 4 " = " }{XPPEDIT 18 0 "y[n]" "6#&%\"yG6#%\"nG" }{TEXT 266 8 " + h * " }{XPPEDIT 18 0 "T^[1]" "6#)%\"TG7#\"\"\"" }{TEXT 267 5 " ( " }{XPPEDIT 18 0 "y[n]" "6#&%\"yG6#%\"nG" }{TEXT 268 34 " , h ) \+ " }}{PARA 4 "" 0 "" {TEXT 269 3 " " }{XPPEDIT 18 0 "y[n+1]" "6#&%\"yG6#,&%\"nG\"\"\"F(F(" }{TEXT 270 4 " = " } {XPPEDIT 18 0 "y[n]" "6#&%\"yG6#%\"nG" }{TEXT 271 8 " + h * " } {XPPEDIT 18 0 "T^[2]" "6#)%\"TG7#\"\"#" }{TEXT 272 5 " ( " } {XPPEDIT 18 0 "y[n]" "6#&%\"yG6#%\"nG" }{TEXT 273 32 " , h ) \+ " }}{PARA 4 "" 0 "" {TEXT 274 3 " " }{XPPEDIT 18 0 " y[n+1]" "6#&%\"yG6#,&%\"nG\"\"\"F(F(" }{TEXT 275 4 " = " }{XPPEDIT 18 0 "y[n]" "6#&%\"yG6#%\"nG" }{TEXT 276 8 " + h * " }{XPPEDIT 18 0 " T^[3]" "6#)%\"TG7#\"\"$" }{TEXT 278 5 " ( " }{XPPEDIT 18 0 "y[n]" "6 #&%\"yG6#%\"nG" }{TEXT 277 15 " , h ) " }}{PARA 4 "" 0 "" {TEXT 279 8 "donde " }{XPPEDIT 18 0 "T^[1]" "6#)%\"TG7#\"\"\"" } {TEXT -1 3 " , " }{XPPEDIT 18 0 "T^[2]" "6#)%\"TG7#\"\"#" }{TEXT -1 3 " y " }{XPPEDIT 18 0 "T^[3]" "6#)%\"TG7#\"\"$" }{TEXT -1 3 " " } {TEXT 280 27 "representan respectivamente" }}{PARA 4 "" 0 "" {TEXT -1 3 " " }{XPPEDIT 18 0 "T^[1]" "6#)%\"TG7#\"\"\"" }{TEXT 283 5 " ( \+ " }{XPPEDIT 18 0 "y[n]" "6#&%\"yG6#%\"nG" }{TEXT 284 12 " , h ) = \+ " }{XPPEDIT 18 0 "f^[0]" "6#)%\"fG7#\"\"!" }{TEXT 281 5 " ( " } {XPPEDIT 18 0 "y[n]" "6#&%\"yG6#%\"nG" }{TEXT 282 4 " ) " }}{PARA 4 " " 0 "" {TEXT -1 3 " " }{XPPEDIT 18 0 "T^[2]" "6#)%\"TG7#\"\"#" } {TEXT 287 5 " ( " }{XPPEDIT 18 0 "y[n]" "6#&%\"yG6#%\"nG" }{TEXT 288 12 " , h ) = " }{XPPEDIT 18 0 "f^[0]" "6#)%\"fG7#\"\"!" }{TEXT 285 5 " ( " }{XPPEDIT 18 0 "y[n]" "6#&%\"yG6#%\"nG" }{TEXT 286 6 " ) + " }{XPPEDIT 18 0 "h/2" "6#*&%\"hG\"\"\"\"\"#!\"\"" }{TEXT -1 1 " \+ " }{TEXT 291 1 " " }{XPPEDIT 18 0 "f^[1]" "6#)%\"fG7#\"\"\"" }{TEXT 289 5 " ( " }{XPPEDIT 18 0 "y[n]" "6#&%\"yG6#%\"nG" }{TEXT 290 3 " ) " }}{PARA 4 "" 0 "" {TEXT -1 3 " " }{XPPEDIT 18 0 "T^[3]" "6#)%\"TG 7#\"\"$" }{TEXT 294 5 " ( " }{XPPEDIT 18 0 "y[n]" "6#&%\"yG6#%\"nG" }{TEXT 295 12 " , h ) = " }{XPPEDIT 18 0 "f^[0]" "6#)%\"fG7#\"\"!" }{TEXT 292 5 " ( " }{XPPEDIT 18 0 "y[n]" "6#&%\"yG6#%\"nG" }{TEXT 293 6 " ) + " }{XPPEDIT 18 0 "h/2" "6#*&%\"hG\"\"\"\"\"#!\"\"" } {TEXT -1 1 " " }{TEXT 298 1 " " }{XPPEDIT 18 0 "f^[1]" "6#)%\"fG7#\"\" \"" }{TEXT 296 5 " ( " }{XPPEDIT 18 0 "y[n]" "6#&%\"yG6#%\"nG" } {TEXT 297 6 " ) + " }{XPPEDIT 18 0 "h^2/6" "6#*&%\"hG\"\"#\"\"'!\"\" " }{TEXT -1 1 " " }{TEXT 301 1 " " }{XPPEDIT 18 0 "f^[2]" "6#)%\"fG7# \"\"#" }{TEXT 299 5 " ( " }{XPPEDIT 18 0 "y[n]" "6#&%\"yG6#%\"nG" } {TEXT 300 3 " ) " }}{PARA 4 "" 0 "" {TEXT 302 7 "y las " }{XPPEDIT 18 0 "f^[k]" "6#)%\"fG7#%\"kG" }{TEXT 303 94 " son las derivadas de f(y(x)) substituyendo y'(x) por f . Vienen dadas (las primeras) \+ " }}{PARA 4 "" 0 "" {TEXT 325 29 "para cada componente j por" }} {PARA 4 "" 0 "" {TEXT -1 4 " " }{TEXT 304 2 " " }{XPPEDIT 18 0 "f^ [0] (j)" "6#)%\"fG-7#\"\"!6#%\"jG" }{TEXT 305 4 " = " }{XPPEDIT 18 0 "f^(j)" "6#)%\"fG%\"jG" }{TEXT -1 3 " " }}{PARA 4 "" 0 "" {TEXT -1 4 " " }{TEXT 306 2 " " }{XPPEDIT 18 0 "f^[1](j)" "6#)%\"fG-7#\"\" \"6#%\"jG" }{TEXT 307 3 " = " }{TEXT -1 1 " " }{XPPEDIT 18 0 "f[k]^j" "6#)&%\"fG6#%\"kG%\"jG" }{TEXT -1 2 " " }{XPPEDIT 18 0 "f^k" "6#)%\"f G%\"kG" }{TEXT -1 6 " ( = " }{XPPEDIT 18 0 "Sigma[k=1]^m" "6#)&%&Sigm aG6#/%\"kG\"\"\"%\"mG" }{TEXT -1 3 " " }{XPPEDIT 18 0 "f[k]^j" "6#)& %\"fG6#%\"kG%\"jG" }{TEXT -1 2 " " }{XPPEDIT 18 0 "f^k" "6#)%\"fG%\"k G" }{TEXT -1 3 " )" }}{PARA 4 "" 0 "" {TEXT -1 4 " " }{TEXT 308 2 " " }{XPPEDIT 18 0 "f^[2](j)" "6#)%\"fG-7#\"\"#6#%\"jG" }{TEXT 309 3 " = " }{TEXT -1 1 " " }{XPPEDIT 18 0 "f[kl]^j" "6#)&%\"fG6#%#klG%\"jG " }{TEXT -1 2 " " }{XPPEDIT 18 0 "f^k" "6#)%\"fG%\"kG" }{TEXT -1 2 " \+ " }{XPPEDIT 18 0 "f^l" "6#)%\"fG%\"lG" }{TEXT -1 6 " + " } {XPPEDIT 18 0 "f[k]^j" "6#)&%\"fG6#%\"kG%\"jG" }{TEXT -1 2 " " } {XPPEDIT 18 0 "f[l]^k" "6#)&%\"fG6#%\"lG%\"kG" }{TEXT -1 2 " " } {XPPEDIT 18 0 "f^l" "6#)%\"fG%\"lG" }{TEXT -1 3 " " }}{PARA 4 "" 0 " " {TEXT 310 63 "El \372ltimo de los m\351todos de TAYLOR escritos es e l de orden 3. " }{XPPEDIT 18 0 "T^[3]" "6#)%\"TG7#\"\"$" }{TEXT 311 34 " es justamente el desarrollo de " }{XPPEDIT 18 0 "Delta" "6#%&De ltaG" }{TEXT 312 4 " ( " }{XPPEDIT 18 0 "x[n]" "6#&%\"xG6#%\"nG" } {TEXT 313 3 " , " }{XPPEDIT 18 0 "y[n]" "6#&%\"yG6#%\"nG" }{TEXT 314 13 " , h ) hasta" }}{PARA 4 "" 0 "" {TEXT 315 18 "dejar el resto en \+ " }{XPPEDIT 18 0 "O(h^3)" "6#-%\"OG6#*$%\"hG\"\"$" }{TEXT 316 2 " " } }}{EXCHG {PARA 4 "" 0 "" {TEXT 319 41 "Diferenciales elementales que i ntervienen" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 4 "" 0 "" {TEXT -1 7 "P ara " }{XPPEDIT 18 0 "f^[0]" "6#)%\"fG7#\"\"!" }{TEXT -1 25 " ya es t\341n f[1] y f[2]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "F0 [1]:=unapply(f[1](y1,y2),y1,y2):\nF0[2]:=unapply(f[2](y1,y2),y1,y2):" }}}{EXCHG {PARA 4 "" 0 "" {TEXT -1 7 "Para " }{XPPEDIT 18 0 "f^[1]" "6#)%\"fG7#\"\"\"" }{TEXT -1 2 " " }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 321 "f1[1]:=unapply(diff(f[1](y1,y2),y1 ),y1,y2):\nf1[2]:=unapply(diff(f[2](y1,y2),y1),y1,y2):\nf2[1]:=unapply (diff(f[1](y1,y2),y2),y1,y2):\nf2[2]:=unapply(diff(f[2](y1,y2),y2),y1, y2):\nF1[1]:=unapply(f1[1](y1,y2)*f[1](y1,y2)+f2[1](y1,y2)*f[2](y1,y2) ,y1,y2):\nF1[2]:=unapply(f1[2](y1,y2)*f[1](y1,y2)+f2[2](y1,y2)*f[2](y1 ,y2),y1,y2):" }}}{EXCHG {PARA 4 "" 0 "" {TEXT -1 7 "Para " } {XPPEDIT 18 0 "f^[2]" "6#)%\"fG7#\"\"#" }{TEXT -1 2 " " }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 857 "f11[1]:=unapply(d iff(f1[1](y1,y2),y1),y1,y2):\nf11[2]:=unapply(diff(f1[2](y1,y2),y1),y1 ,y2):\nf12[1]:=unapply(diff(f1[1](y1,y2),y2),y1,y2):\nf12[2]:=unapply( diff(f1[2](y1,y2),y2),y1,y2):\nf22[1]:=unapply(diff(f2[1](y1,y2),y2),y 1,y2):\nf22[2]:=unapply(diff(f2[2](y1,y2),y2),y1,y2):\nF2[1]:=unapply( f11[1](y1,y2)*f[1](y1,y2)*f[1](y1,y2)+2*f12[1](y1,y2)*f[1](y1,y2)*f[2] (y1,y2)+f22[1](y1,y2)*f[2](y1,y2)*f[2](y1,y2)+f1[1](y1,y2)*f1[1](y1,y2 )*f[1](y1,y2)+f2[1](y1,y2)*f1[2](y1,y2)*f[1](y1,y2)+f1[1](y1,y2)*f2[1] (y1,y2)*f[2](y1,y2)+f2[1](y1,y2)*f2[2](y1,y2)*f[2](y1,y2),y1,y2):\nF2[ 2]:=unapply(f11[2](y1,y2)*f[1](y1,y2)*f[1](y1,y2)+2*f12[2](y1,y2)*f[1] (y1,y2)*f[2](y1,y2)+f22[2](y1,y2)*f[2](y1,y2)*f[2](y1,y2)+f1[2](y1,y2) *f1[1](y1,y2)*f[1](y1,y2)+f2[2](y1,y2)*f1[2](y1,y2)*f[1](y1,y2)+f1[2]( y1,y2)*f2[1](y1,y2)*f[2](y1,y2)+f2[2](y1,y2)*f2[2](y1,y2)*f[2](y1,y2), y1,y2):" }}}{EXCHG {PARA 4 "" 0 "" {TEXT -1 6 " ahora" }{MPLTEXT 1 0 1 " " }{XPPEDIT 18 0 "T^[3]" "6#)%\"TG7#\"\"$" }{TEXT 322 5 " ( " } {XPPEDIT 18 0 "y[n]" "6#&%\"yG6#%\"nG" }{TEXT 321 7 " , h ) " }{TEXT 323 3 " es" }{TEXT 324 1 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 151 "T3[1]:=unapply(F0[1](y1,y2)+(h/2)*F1[1](y1,y2)+(h^2/6)*F2[1](y1,y 2),y1,y2):\nT3[2]:=unapply(F0[2](y1,y2)+(h/2)*F1[2](y1,y2)+(h^2/6)*F2[ 2](y1,y2),y1,y2):" }}}{EXCHG {PARA 4 "" 0 "" {TEXT -1 25 "Funciones qu e intervienen" }{TEXT 326 1 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "print(`1f=`,f[1](y[1],y[2])):print(`2f=`,f[2](y[1],y[2])):" }} {PARA 11 "" 1 "" {XPPMATH 20 "6$%$1f=G*&,&*$)&%\"yG6#\"\"\"\"\"#F+!\" \"*$)&F)6#F,\"\"%F+F+F+F0!\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%$2f= G,$*&&%\"yG6#\"\"\"F)&F'6#\"\"#!\"\"F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 128 "print(`1f_1=`,f1[1](y[1],y[2])):print(`2f_1=`,f1[2]( y[1],y[2])):print(`1f_2=`,f2[1](y[1],y[2])):print(`1f_1=`,f2[2](y[1],y [2])):" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%&1f_1=G,$*&&%\"yG6#\"\"\"F) &F'6#\"\"#!\"#F-" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%&2f_1=G,$*&\"\"\" F&&%\"yG6#\"\"#!\"\"F+" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%&1f_2=G,&&% \"yG6#\"\"#\"\"%*(F(\"\"\",&*$)&F&6#F+F(F+!\"\"*$)F%F)F+F+F+F%!\"$F1" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%&1f_1=G*&&%\"yG6#\"\"\"F(&F&6#\"\"# !\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 204 "print(`1f_11=`,f11 [1](y[1],y[2])):print(`2f_11=`,f11[2](y[1],y[2])):print(`1f_12=`,f12[1 ](y[1],y[2])):print(`2f_12=`,f12[2](y[1],y[2])):print(`1f_22=`,f22[1]( y[1],y[2])):print(`2f_22=`,f22[2](y[1],y[2])):" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%'1f_11=G,$*&\"\"\"F&*$)&%\"yG6#\"\"#F,F&!\"\"!\"#" }} {PARA 11 "" 1 "" {XPPMATH 20 "6$%'2f_11=G\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%'1f_12=G,$*&&%\"yG6#\"\"\"F)&F'6#\"\"#!\"$\"\"%" }} {PARA 11 "" 1 "" {XPPMATH 20 "6$%'2f_12=G*&\"\"\"F%*$)&%\"yG6#\"\"#F+F %!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%'1f_22=G,&!\"%\"\"\"*(\"\"' F&,&*$)&%\"yG6#F&\"\"#F&!\"\"*$)&F-6#F/\"\"%F&F&F&F3F%F&" }}{PARA 11 " " 1 "" {XPPMATH 20 "6$%'2f_22=G,$*&&%\"yG6#\"\"\"F)&F'6#\"\"#!\"$!\"# " }}}{EXCHG {PARA 4 "" 0 "" {TEXT -1 48 "Estamos en condiciones de com enzar con el m\351todo" }{TEXT 328 1 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "x0:=0;y0:=[0.,1.];h:=0.1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#x0G\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#y0G7$ $\"\"!F'$\"\"\"F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"hG$\"\"\"!\" \"" }}}{EXCHG {PARA 4 "" 0 "" {TEXT 327 11 "Primer paso" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "x1:=x0+h;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#x1G$\"\"\"!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "print(`1f=`,f[1](y0[1],y0[2])):print(`2f=`,f[2]( y0[1],y0[2])):" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%$1f=G$\"$+\"!\"#" } }{PARA 11 "" 1 "" {XPPMATH 20 "6$%$2f=G$!\"!\"\"!" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 136 "print(`1f_1=`,f1[1](y0[1],y0[2])):print(`2f _1=`,f1[2](y0[1],y0[2])):print(`1f_2=`,f2[1](y0[1],y0[2])):print(`1f_1 =`,f2[2](y0[1],y0[2])):" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%&1f_1=G$! \"!\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%&2f_1=G$!\"\"\"\"!" }} {PARA 11 "" 1 "" {XPPMATH 20 "6$%&1f_2=G$\"$+#!\"#" }}{PARA 11 "" 1 " " {XPPMATH 20 "6$%&1f_1=G$\"\"!F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 216 "print(`1f_11=`,f11[1](y0[1],y0[2])):print(`2f_11=`,f 11[2](y0[1],y0[2])):print(`1f_12=`,f12[1](y0[1],y0[2])):print(`2f_12=` ,f12[2](y0[1],y0[2])):print(`1f_22=`,f22[1](y0[1],y0[2])):print(`2f_22 =`,f22[2](y0[1],y0[2])):" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%'1f_11=G$ !\"#\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%'2f_11=G\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%'1f_12=G$\"\"!F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%'2f_12=G$\"\"\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6$%'1f_22=G$\"$+#!\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%'2f_22=G$!\" !\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "print(`1f[0]=`,F0 [1](y0[1],y0[2])):print(`2f[0]=`,F0[2](y0[1],y0[2])):" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%'1f[0]=G$\"$+\"!\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%'2f[0]=G$!\"!\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "print(`1f[1]=`,F1[1](y0[1],y0[2])):print(`2f[1]=`,F1[2](y0[1],y0[2 ])):" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%'1f[1]=G$!\"!\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%'2f[1]=G$!$+\"!\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "print(`1f[2]=`,F2[1](y0[1],y0[2])):print(`2f[2]= `,F2[2](y0[1],y0[2])):" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%'1f[2]=G$!$ +%!\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%'2f[2]=G$!\"!\"\"!" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "T3[1](y0[1],y0[2]);T3[2](y0[ 1],y0[2]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"$$**!\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$!$+&!\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "y1[1]:=y0[1]+h*T3[1](y0[1],y0[2]);y1[2]:=y0[2]+h*T3[2 ](y0[1],y0[2]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%#y1G6#\"\"\"$\"$ $**!\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%#y1G6#\"\"#$\"$&**!\"$" }}}{EXCHG {PARA 4 "" 0 "" {TEXT 317 12 "Segundo paso" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "y0:=y1;x1:=x1+h;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#y0G%#y1G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#x1G$\"\"#!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "T3[1](y0[1],y0[2]);T3[2](y0[1],y0[2]);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#$\"$`*!\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$! $]\"!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "y1[1]:=y0[1]+h* T3[1](y0[1],y0[2]);y1[2]:=y0[2]+h*T3[2](y0[1],y0[2]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%#y1G6#\"\"\"$\"$&>!\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%#y1G6#\"\"#$\"$q*!\"$" }}}{EXCHG {PARA 4 "" 0 "" {TEXT 318 11 "Tercer paso" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "y0:=y1;x1:=x1+h;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#y0G%#y1G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#x1G$\"\"$!\"\" " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "T3[1](y0[1],y0[2]);T3[2 ](y0[1],y0[2]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"$b)!\"$" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#$!$]#!\"$" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 68 "y1[1]:=y0[1]+h*T3[1](y0[1],y0[2]);y1[2]:=y0[2]+h*T3 [2](y0[1],y0[2]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%#y1G6#\"\"\"$ \"$!G!\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%#y1G6#\"\"#$\"$O*!\"$ " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "yv[1](x1)-y1[1];yv[2](x 1)-y1[2];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"\"$!\"$" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#$\"#>!\"$" }}}}{MARK "0 0 0" 13 }{VIEWOPTS 1 1 0 3 4 1802 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }