Help me to solve this differential equation!?

Question

I have this differential equation

[y''(x)]^3 + x*y''(x) = 2*y'(x)

y''(x) - is the second derivative and y'(x) is the first derivative and the goal is to find y(x). * means multiplying.

Please help me with this one.

Answer 1

Did you erase my answer? Well it is gone now. I did remember one trick but I can't seem tomake it work, that cubed term gets int he way. One method was to turn a d.e. into a linera system then use the exponetial of the matrix. E.g., if y"+y=0 then you set a=y,b=y' then you get a'=b and b'=-a so [a,b]'=[[0,1],[-1,0]]*[a,b] so then [a,b]=exp(matrix*t)....but that y"^3 is gonna mess things up big-time.