# Working with Differential Equations

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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)

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<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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