# First order nonlinear ordinary differential equation

1. Jul 6, 2010

1. The problem statement, all variables and given/known data

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)).

2. Relevant equations

3. 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 ;)

2. Jul 6, 2010

### 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

3. Jul 6, 2010

### 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.

4. Jul 6, 2010