I was given the following ODE to solve and it seemed simple enough. However, after you have used the integrating factor the integral is not integratable.(adsbygoogle = window.adsbygoogle || []).push({});

y' = (1+x^2)y +x^3, y(0)=0

Find y(1) if y(x) is the solution to the above ODE.

So I put it in the proper form of:

y' + (-1-x^2)y = x^3

INT FACTOR = e^(INTEGRAL(-1-x^2) dx) = e^(-x^3/3 - x) so:

y = e^(x/3 + x) * (INTEGRAL e^(-x/3 - x) * x^3 dx + C)

This"(INTEGRAL e^(-x/3 - x)"is not integratable by any means I know of. So I e-mailed the Professor and this is what he told me to do.

"I gave this problem so you would have experience with something that doesn't have an explicit solution. The solution is in terms of an integral.You can even make it a definite integral with the upper limit variable. Choose the lower limit so the initial condition works out. Since your calculator can do numerical integration, you can then evaluate y(1)."

I am clueless on what he is talking about. I have looked in all of the DE texts I have and all say that it is fine to leave it in the form that it is in. However, none of those examples cover what to do when there are initial conditions present and you run into this problem.

Can anyone help me with this?

Thanks, Steve

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# Integrating Factor and Unintegratable Term

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