# Find a general solution y (x) of non-homogeneous linear equations of the 2nd order with constant coefficients and special right side. How to solve? (pictures below) Thank you a lot!

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here:

this should be solution

here:

this should be solution

##### 1 Answer

Solve the differential equation:

This is a non-homogeneous linear equation with constant coefficients, so we start by solving the characteristic equation of the corresponding homogeneous equation:

So the general solution of the homogeneous equation is:

In the complete equation, the known term is in the form

As

where

Then:

and equating the coefficients of the same degree in

So:

and the complete solution is: