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-   -   Finding the solution to an IVP Problem. Basic Differential Equations problem. (http://www.physicsforums.com/showthread.php?t=506419)

 cyturk Jun12-11 07:43 PM

Finding the solution to an IVP Problem. Basic Differential Equations problem.

I am trying to solve an IVP problem and I seem to be stuck on it because I am getting an integration that seems very complicated and I think I messed up on it, I have my work so far below.

1. The problem statement, all variables and given/known data

Find the solution to the IVP

ty^'+7y=2t^2 e^2t, y(1)=7

Is this equation linear? Determine in what interval the solutions exist.

2. Relevant equations

3. The attempt at a solution

http://i.imgur.com/rs1nk.jpg

The image has my work so far, as you can see the integration for (t^7)(2te^2t) is a beast and that is why I think I am wrong so far. Here is the integration answer http://www.wolframalpha.com/input/?i=integrate+%28t^7%29%282te^%282t%29%29.

 JJacquelin Jun13-11 01:13 AM

Re: Finding the solution to an IVP Problem. Basic Differential Equations problem.

The primitives of (t^8)exp(2t) are on the form P(x)exp(2t) were P(x) is a 8th degree polynomial.
Derive this function and find the coefficients of the polynomial by indentification with (t^8)exp(2t)

 hunt_mat Jun13-11 05:09 AM

Re: Finding the solution to an IVP Problem. Basic Differential Equations problem.

You started out very well, and from:
$$\frac{d}{dt}(t^{7}y)=2t^{8}e^{2t}$$
I think you have made an error, you can do two things: 1) You can do an indefinite integration and add an integration constant and find that constand by using the initial condition or 2) integrate from 1 to t both sides and use Y(1)=7.

 HallsofIvy Jun13-11 06:50 AM

Re: Finding the solution to an IVP Problem. Basic Differential Equations problem.

Integrate 2t8e2t using integration by parts- 8 times!

 cyturk Jun26-11 03:22 PM

Re: Finding the solution to an IVP Problem. Basic Differential Equations problem.

Quote:
 Quote by HallsofIvy (Post 3354240) Integrate 2t8e2t using integration by parts- 8 times!
Thanks for everyone else and this is what I ended up doing. It was the correct way of solving the problem even though it was a little bit of a hassle! :)

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