Hi,

I was wondering if someone could take five minutes to explain how you work out the general solution to an equation. I sort of understand it but is there a way i can look at an equation and instantly recognise that a particular equation has a certain solution. For instance:

dy/dx = 3(x -1)^2 + 20(y-(x-1)^3)

has the general solution:

y(x) = (x-1)^3 + Ae^20x

How would i go about finding that?

Does it depend on then inital conditions and the boundary conditions?

Cheers for the help.