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Question: integral of solution of differential equation

Question:integral of solution of differential equation

STHence 50 Maple 15
March 02 2013
1

Hi all,

I have a differential equation as follows:

x(t)^2+cos(x(t))+diff(x(t), t)+diff(x(t), t, t) = 100

x(0)=2, D(x)(0) = 3;

After using "dsolve" to solve this equation, the solution x(t) is obtained.

How can we obtain the following function?

g(k) = 0∫kx2(t)dt

How can we plot the function g(k) when k = 0 ..10?

I tried many ways, but I'm only able to obtain the derivative of x(t), not the integral of x2(t). My Maple file is attached in this post.

Thank you so much. 

STHence

integral_of_solutio.mw
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