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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)

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 - ...

#### Solution Summary

Step by step guide to the final answer.

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