# Homework Help: Riccati Equation

1. Mar 4, 2013

### astrofunk21

1. The problem statement, all variables and given/known data
Find the general solutions of the following 1st-order DE: y' = by2+(1/4bx2) where b ≠ 0 is a constant.

2. Relevant equations
Now this is a Riccati Equation, I know that. In my math class we've only learned to solve DEs the following ways:
a. Separation of Variables
b. Substitution
i. Polynomial Substitution
ii. Homogeneous Substitution
iii. Bernoulli DE

3. The attempt at a solution
The first thing I did was to assume a particular solution, which I made y1 = A/x With this I found the derivative of it: y' = -A/x2 and then y2 = A2/x2

Using these I subbed them into the original equation giving me:
-A/x2 = bA2/x2 + 1/4bx2

After this I solved to make it equal to zero which is:
0 = A + bA2 + 1/4b

From this I used the quadratic formula to get:
A = 0 and A = -1/b

After this I don't know where to go, I don't know if those are even right. Could anyone give me some direction and at the same time check if what I have so far is right?

2. Mar 4, 2013

Anything?

3. Mar 5, 2013

### astrofunk21

Is it that hard? Haha