First order nonlinear ordinary differential equation

[MadMathMan]

Homework Statement

y' + Ay² = B

A & B are constants and y is a function of x

Find the general solution to the differential equation. (Find y(x)).

Homework Equations

The Attempt at a Solution

This differential equation came up when I was trying to solve a problem in physics. I have just learned to solve basic linear differential equations from high school and don't know how to start solving this or even if it's solvable without a computer. If somebody could give me a push in the right direction or tell me what I could study to be able to solve it, it would have been very nice :)

The only thing I've tried is differentiating it with respect to x, and getting this:

y'' + 2Ayy' = 0

I don't find this any easier because I have the y×y' there. So, any help would be nice ;)

 

[hunt_mat]

Write the ODe in the following way:
$$\frac{dy}{dx}=B-Ay^{2}$$
This equation is separable, divide by $$B-Ay^{2}$$ and integrate

Mat

 

[tmccullough]

This one is "separable" - which means it's solvable using integration. Rearrange to get
$$\frac{dy}{B-Ay^2} = dx,$$
and do two integrals. There will be significant algebraic rearrangement involved to solve for y in terms of x.

You should probably reference a differential equations book.

 

[MadMathMan]

Thanks for the answers!
That was really less painful than I expected Don't know why I didn't think of that
Next problem now is solving the integral, but I think I should be able to do that myself