y'' - 4y = xe^(x)
Use the method of vartiation of parameters to find the general solution of the given differential equation.
First solve the homogeneous equation .
The characteristic equation is .
Thus, the complimentary solution is .
Now, let and .
We now need to find and
Thus,
I leave it for you to find (See spoiler to check your answer).
Spoiler:
Thus,
I leave it for you to find (See spoiler to check your answer).
Spoiler:
Once you find and , the solution to your differential equation would be (See spoiler to check your answer)
Spoiler: