Hi, all got a Question im a bit stuck on need a lil help if possible.

X^3(d^3 y/dx^3)-3X^2(d^2 y/dx^2)+6x(dy/dx)-6y = 0

can be written as y = c1(X)+c2(x^2)+c3(x^3)

for choices of the arbitrary constants solve the initial value problem which consists of the above differential equation and the three conditions y(2)=0, y’(2)=2 and y’’(2)=2, where the ‘ denotes differentiation with respect to x.

i tried to differinate the 2nd equation 3 times, and then just using algebra to try find c1 c2 and c3 with the 3 equations i came up with, but im notsure where im ment to be heading with this.

im not quite i understand what the question is asking so any help is appreciated

Thanks