{VERSION 5 0 "SUN SPARC SOLARIS" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with(DE tools):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "dsolve(D(y)(x)=y (x)+(y(x))^3); # y' = y + y^3 - general solution" }}{PARA 11 "" 1 " " {XPPMATH 20 "6$/-%\"yG6#%\"xG*&\"\"\"F)*$,&F)!\"\"*&-%$expG6#,$*&\" \"#F)F'F)F,F)%$_C1GF)F)#F)F3F,/F$,$F(F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "dsolve(\{ D(y)(x)=y(x)+(y(x))^3, y(0)=2 \} ); # IV P with initial condition" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"yG6#% \"xG*&\"\"\"F)*$,&F)!\"\"*&#\"\"&\"\"%F)-%$expG6#,$*&\"\"#F)F'F)F,F)F) #F)F6F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "y(x) := 1/((-1+2 *exp(-2*x)/exp(-2))^(1/2));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"yG 6#%\"xG*&\"\"\"F)*$,&F)!\"\"*(\"\"#F)-%$expG6#,$*&F.F)F'F)F,F)-F06#!\" #F,F)#F)F.F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 79 "simplify(di ff(y(x),x) - (y(x) + (y(x))^3)); # check DE by differentiating y(x)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "8 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }