Please show me full answer for this one ind the general solu

Please show me full answer for this one:

ind the general solution of the given second order differential equation 9Xy 20y 5x

First we solve the homogeneous ODE

x^2y\'\'+9xy\'-20y=0

Let, y=x^r

Substituting gives

r(r-1)+9r-20=0

r^2+8r-20=0

r^2+10r-2r-20=0

r=-10,2

So, general solution to homogeneous ODE is

yh= a/x^{10}+bx^2

Now let particular solution be: c/x

Substituting gives

2c/x-9c/x-20c/x=5/x

-27c/x=5/x

c=-5/27

So general solution is

y(x)=a/x^{10}+bx^2-5/(27x)