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

  1. 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


    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^7%29%282te^%282t%29%29.
  2. jcsd
  3. 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)
  4. hunt_mat

    hunt_mat 1,621
    Homework Helper

    You started out very well, and from:
    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.
  5. HallsofIvy

    HallsofIvy 41,268
    Staff Emeritus
    Science Advisor

    Integrate 2t8e2t using integration by parts- 8 times!
  6. 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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