Hi experts, I need your help to find higher-order prolongation(extended infinitesimals) with the help of infinitesimals. rhelp1.mw

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in MAPLE. I have attached a worksheet please check it.

Kindly help me to find it

Thank you.

I have attached a maplework please check it. I want to solution graph by using RK 4th order with shooting technique or RK Fehlberg method. help.mw

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Please help to find the exact solution of any ODE by the >sinh or cosh method. I have attached arbitrary ODE here:

>ode:=U""+c^2*U"+k*c*U"-(3U^2+a)*U''=0