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General solution of nonhomogenous 2nd order linear differential equations

Please find the general solution of the nonhomogenous second order linear differential equation below by following these steps:

1. Find the general solution y= C1y1 + C2y2 of the associated homogenous equation (complementary solution)
2. Find a single solution of yp of above.(particular solution).
3. Express the general solution in the form y=yp + C1y1 +C2y2

Please show all steps. Thank you.

d²y/dx² - 4y = e^(3x)

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The general solution of a nonhomogenous 2nd order linear differential equation is found. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.