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. 
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) 
Re: Finding the solution to an IVP Problem. Basic Differential Equations problem.
You started out very well, and from:
[tex] \frac{d}{dt}(t^{7}y)=2t^{8}e^{2t} [/tex] 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. 
Re: Finding the solution to an IVP Problem. Basic Differential Equations problem.
Integrate 2t^{8}e^{2t} using integration by parts 8 times!

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