# Homework Help: Differential Equations homework problem.

1. May 27, 2010

### tarmon.gaidon

1. The problem statement, all variables and given/known data
The equation $$\frac{dy}{dx}$$ = A(x)y2+B(x)y+C(x) is called a Riccati equation. Suppose that one particular solution y1(x) of this equation is known. Show that the substitution

y = y1+$$\frac{1}{v}$$

transforms the Riccati equation into the linear equation

$$\frac{dv}{dx}$$+ (B+2Ay1)v = -A.

3. The attempt at a solution

So i know that y' = y1' - $$\frac{v'}{v^2}$$ and I have tried substituting y and y' back into the original equation in order to simplify it down to the linear equation given. Unfortunately for some reason I am not getting anywhere. Any help would be appreciated!

Thanks,
Rob

P.S. Sorry for the crappy formatting, not really sure what I am doing.

2. May 27, 2010

### Staff: Mentor

When you make your substitution, the left side will be dy1/dx - v'/v. Are you remembering to replace dy1/dx by A(x)y12 + B(x)y1 + C(x)?