# Working with Differential Equations

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)

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#### 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 - ...

#### Solution Summary

Step by step guide to the final answer.

$2.49