How to make Maple to integrate term by term?

Question:How to make Maple to integrate term by term?

Posted: emendes 445 Product: Maple 2017

November 08 2019

Hello

I wonder how integrate can be applied term by term to the following nonlinear differential equation

(diff(y(t), t))*(diff(y(t), t, t, t))-(diff(y(t), t))*y(t)^2-(diff(y(t), t))*(diff(y(t), t, t))-(diff(y(t), t))*A*y(t)

The expected output will be something like

(diff(y(t), t))*(diff(y(t), t, t))-(1/3)*y(t)^3-(1/2)*A*y(t)^2-(1/2)*(diff(y(t), t))^2+C+int((diff(y(s), s, s))^2, s = 0 .. t)

map(x-> integrate(x,t),(diff(y(t), t))*(diff(y(t), t, t, t))-(diff(y(t), t))*y(t)^2-(diff(y(t), t))*(diff(y(t), t, t))-(diff(y(t), t))*A*y(t))

solves most of it but not the first part.

Many thanks

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