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    Working with Differential Equations

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    Hi,

    For this problem please state the method you used and show the work required to obtain the answer.

    Find the complete solution to this equation problem.

    y^3 - 2y^2 + y^1 = 2- 24e^(x) + 40e^(5x)

    © BrainMass Inc. brainmass.com March 4, 2021, 5:42 pm ad1c9bdddf
    https://brainmass.com/math/calculus-and-analysis/working-with-differential-equations-7027

    Solution Preview

    <br>y^3 - 2y^2 + y^1 = 2- 24e^(x) + 40e^(5x) ....(1)
    <br>
    <br>
    <br>First set the right side equal to 0 and find the solution as in the
    <br>case of a homogeneous equation (this is called complementary function
    <br>y1) and then by trial find a particular solution (particular integral
    <br>y2)
    <br>
    <br>Now the general solution is given by,
    <br>
    <br> Y = y1 + y2
    <br>
    <br>First evaluate y1
    <br>................
    <br>
    <br>y^3 - 2y^2 + y^1 = 0
    <br>
    <br>ie, y (y^2 - ...

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