# General solution of non-homogenous second order linear differential equations : dÂ²y/dxÂ² + y = cosx

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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.

dÂ²y/dxÂ² + y = cosx

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#### Solution Summary

The general solution of a non-homogenous second order linear differential equation is found. The solution is detailed and well presented.

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