I need to solve this:
x3y‴
I know that first I have to solve:
E = x^3y''' - x^2y'' + 2xy' - 2y = 0
I choose y = x^r. By feeding that to E it will lead me to the following characteristic equation:
(r-2)(r-1)^2=0
Now if all roots would be distinct the solution would be simple, but with repeating roots how do I approach this equation?
I know that the correct answer must be:
y(x) = c_3 x^2+c_1 x+c_2 x ln(x)+x^3/4
I don't know how to get to the c_2xln(x) part. I know that I have to use Wronskian matrix to get the x^3/4 part.