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-KUTTA" }}{PARA 4 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT 259 15 "Ejercicio 05-01" }}{PARA 4 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 " " {TEXT -1 33 "Para el problema de segundo orden" }}{PARA 4 "" 0 "" {TEXT -1 16 " y'' + y = 0" }}{PARA 4 "" 0 "" {TEXT -1 26 " y(0 ) = 0 , y'(0) = 1" }}{PARA 4 "" 0 "" {TEXT -1 51 "y convertido en el \+ problema tipo aut\363nomo de Cauchy" }}{PARA 4 "" 0 "" {TEXT -1 17 " \+ y'_1 = y_2 " }}{PARA 4 "" 0 "" {TEXT -1 17 " y'_2 = - y_1" }} {PARA 4 "" 0 "" {TEXT -1 28 " y_1(0) = 0 , y_2(0) = 1" }}{PARA 4 " " 0 "" {TEXT -1 104 "(de soluci\363n exacta y_1(x) = sen(x) , y_2(x) = cos(x) , o sea y(x) = sen(x) ) util\355cese el m\351todo de " }} {PARA 4 "" 0 "" {TEXT -1 18 "TAYLOR de orden 3 " }{TEXT 256 73 "para a proximar 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 ope raciones 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 "E l sistema (aut.) y la verdadera soluci\363n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "f[1]:=unapply(y2,y1,y2):\nf[2]:=unapply(-y1,y1,y2) :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "yv[1]:=unapply(sin(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 268 64 "Los m\351todos de TAYLOR para sistemas aut\363nomos y \+ en los primeros " }}{PARA 4 "" 0 "" {TEXT 322 34 "\363rdenes se escrib en vectorialmente" }}{PARA 4 "" 0 "" {TEXT 269 4 " " }{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^[1]" "6#)%\"TG7#\"\"\"" }{TEXT 272 5 " ( " } {XPPEDIT 18 0 "y[n]" "6#&%\"yG6#%\"nG" }{TEXT 273 34 " , 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^[2]" "6#)%\"TG7#\"\"#" }{TEXT 277 5 " ( " } {XPPEDIT 18 0 "y[n]" "6#&%\"yG6#%\"nG" }{TEXT 278 32 " , h ) \+ " }}{PARA 4 "" 0 "" {TEXT 279 3 " " }{XPPEDIT 18 0 " y[n+1]" "6#&%\"yG6#,&%\"nG\"\"\"F(F(" }{TEXT 280 4 " = " }{XPPEDIT 18 0 "y[n]" "6#&%\"yG6#%\"nG" }{TEXT 281 8 " + h * " }{XPPEDIT 18 0 " T^[3]" "6#)%\"TG7#\"\"$" }{TEXT 283 5 " ( " }{XPPEDIT 18 0 "y[n]" "6 #&%\"yG6#%\"nG" }{TEXT 282 15 " , h ) " }}{PARA 4 "" 0 "" {TEXT 284 8 "donde " }{XPPEDIT 18 0 "T^[1]" "6#)%\"TG7#\"\"\"" } {TEXT -1 3 " , " }{XPPEDIT 18 0 "T^[2]" "6#)%\"TG7#\"\"#" }{TEXT -1 3 " y " }{XPPEDIT 18 0 "T^[3]" "6#)%\"TG7#\"\"$" }{TEXT -1 3 " " } {TEXT 285 27 "representan respectivamente" }}{PARA 4 "" 0 "" {TEXT -1 3 " " }{XPPEDIT 18 0 "T^[1]" "6#)%\"TG7#\"\"\"" }{TEXT 288 5 " ( \+ " }{XPPEDIT 18 0 "y[n]" "6#&%\"yG6#%\"nG" }{TEXT 289 12 " , h ) = \+ " }{XPPEDIT 18 0 "f^[0]" "6#)%\"fG7#\"\"!" }{TEXT 286 5 " ( " } {XPPEDIT 18 0 "y[n]" "6#&%\"yG6#%\"nG" }{TEXT 287 4 " ) " }}{PARA 4 " " 0 "" {TEXT -1 3 " " }{XPPEDIT 18 0 "T^[2]" "6#)%\"TG7#\"\"#" } {TEXT 292 5 " ( " }{XPPEDIT 18 0 "y[n]" "6#&%\"yG6#%\"nG" }{TEXT 293 12 " , h ) = " }{XPPEDIT 18 0 "f^[0]" "6#)%\"fG7#\"\"!" }{TEXT 290 5 " ( " }{XPPEDIT 18 0 "y[n]" "6#&%\"yG6#%\"nG" }{TEXT 291 6 " ) + " }{XPPEDIT 18 0 "h/2" "6#*&%\"hG\"\"\"\"\"#!\"\"" }{TEXT -1 1 " \+ " }{TEXT 296 1 " " }{XPPEDIT 18 0 "f^[1]" "6#)%\"fG7#\"\"\"" }{TEXT 294 5 " ( " }{XPPEDIT 18 0 "y[n]" "6#&%\"yG6#%\"nG" }{TEXT 295 3 " ) " }}{PARA 4 "" 0 "" {TEXT -1 3 " " }{XPPEDIT 18 0 "T^[3]" "6#)%\"TG 7#\"\"$" }{TEXT 299 5 " ( " }{XPPEDIT 18 0 "y[n]" "6#&%\"yG6#%\"nG" }{TEXT 300 12 " , h ) = " }{XPPEDIT 18 0 "f^[0]" "6#)%\"fG7#\"\"!" }{TEXT 297 5 " ( " }{XPPEDIT 18 0 "y[n]" "6#&%\"yG6#%\"nG" }{TEXT 298 6 " ) + " }{XPPEDIT 18 0 "h/2" "6#*&%\"hG\"\"\"\"\"#!\"\"" } {TEXT -1 1 " " }{TEXT 303 1 " " }{XPPEDIT 18 0 "f^[1]" "6#)%\"fG7#\"\" \"" }{TEXT 301 5 " ( " }{XPPEDIT 18 0 "y[n]" "6#&%\"yG6#%\"nG" } {TEXT 302 6 " ) + " }{XPPEDIT 18 0 "h^2/6" "6#*&%\"hG\"\"#\"\"'!\"\" " }{TEXT -1 1 " " }{TEXT 306 1 " " }{XPPEDIT 18 0 "f^[2]" "6#)%\"fG7# \"\"#" }{TEXT 304 5 " ( " }{XPPEDIT 18 0 "y[n]" "6#&%\"yG6#%\"nG" } {TEXT 305 3 " ) " }}{PARA 4 "" 0 "" {TEXT 307 7 "y las " }{XPPEDIT 18 0 "f^[k]" "6#)%\"fG7#%\"kG" }{TEXT 308 94 " son las derivadas de f(y(x)) substituyendo y'(x) por f . Vienen dadas (las primeras) \+ " }}{PARA 4 "" 0 "" {TEXT 323 29 "para cada componente j por" }} {PARA 4 "" 0 "" {TEXT -1 4 " " }{TEXT 309 2 " " }{XPPEDIT 18 0 "f^ [0] (j)" "6#)%\"fG-7#\"\"!6#%\"jG" }{TEXT 310 4 " = " }{XPPEDIT 18 0 "f^(j)" "6#)%\"fG%\"jG" }{TEXT -1 3 " " }}{PARA 4 "" 0 "" {TEXT -1 4 " " }{TEXT 311 2 " " }{XPPEDIT 18 0 "f^[1](j)" "6#)%\"fG-7#\"\" \"6#%\"jG" }{TEXT 312 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 313 2 " " }{XPPEDIT 18 0 "f^[2](j)" "6#)%\"fG-7#\"\"#6#%\"jG" }{TEXT 314 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 315 63 "El \372ltimo de los m\351todos de TAYLOR escritos es e l de orden 3. " }{XPPEDIT 18 0 "T^[3]" "6#)%\"TG7#\"\"$" }{TEXT 316 34 " es justamente el desarrollo de " }{XPPEDIT 18 0 "Delta" "6#%&De ltaG" }{TEXT 317 4 " ( " }{XPPEDIT 18 0 "x[n]" "6#&%\"xG6#%\"nG" } {TEXT 318 3 " , " }{XPPEDIT 18 0 "y[n]" "6#&%\"yG6#%\"nG" }{TEXT 319 13 " , h ) hasta" }}{PARA 4 "" 0 "" {TEXT 320 18 "dejar el resto en \+ " }{XPPEDIT 18 0 "O(h^3)" "6#-%\"OG6#*$%\"hG\"\"$" }{TEXT 321 2 " " } }}{EXCHG {PARA 4 "" 0 "" {TEXT 263 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#\"\"$" }{TEXT 265 5 " ( " } {XPPEDIT 18 0 "y[n]" "6#&%\"yG6#%\"nG" }{TEXT 264 7 " , h ) " }{TEXT 266 3 " es" }{TEXT 267 1 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 151 "T3[1]:=unapply(F0[1](y1,y2)+(h/2)*F1[1](y1,y2)+(h^2/6)*F2[1](y1,y 2),y1,y2):\nT3[2]:=unapply(F0[2](y1,y2)+(h/2)*F1[2](y1,y2)+(h^2/6)*F2[ 2](y1,y2),y1,y2):" }}}{EXCHG {PARA 4 "" 0 "" {TEXT -1 25 "Funciones qu e intervienen" }{TEXT 326 1 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "print(`1f=`,f[1](y[1],y[2])):print(`2f=`,f[2](y[1],y[2])):" }} {PARA 11 "" 1 "" {XPPMATH 20 "6$%$1f=G&%\"yG6#\"\"#" }}{PARA 11 "" 1 " " {XPPMATH 20 "6$%$2f=G,$&%\"yG6#\"\"\"!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 128 "print(`1f_1=`,f1[1](y[1],y[2])):print(`2f_1=`,f 1[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$%&1f_1=G\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%&2f_1=G!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%&1f_2=G\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%&1f_1=G\"\"! " }}}{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$%'1f_11=G\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%'2f_ 11=G\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%'1f_12=G\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%'2f_12=G\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%'1f_22=G\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%'2f_22=G\"\"! " }}}{EXCHG {PARA 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(`2 f_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\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 216 "print(`1f_1 1=`,f11[1](y0[1],y0[2])):print(`2f_11=`,f11[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$%'1f_ 12=G\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%'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 "pri nt(`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],y 0[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 $%'2f[2]=G$\"\"!F%" }}}{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]);y 1[2]:=y0[2]+h*T3[2](y0[1],y0[2]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> &%#y1G6#\"\"\"$\"$)**!\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%#y1G6# \"\"#$\"$&**!\"$" }}}{EXCHG {PARA 4 "" 0 "" {TEXT 324 12 "Segundo paso " }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "y0:= y1;x1:=x1+h;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#y0G%#y1G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#x1G$\"\"#!\"\"" }}}{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 325 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#$\"$e*!\"$" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#$!$[#!\"$" }}}{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#\"\"\"$ \"$&H!\"$" }}{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" 11 }{VIEWOPTS 1 1 0 3 4 1802 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }