# Ordinary Differential Equations

1. Jan 9, 2013

### aaronfue

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

y = 2xy' + y(y')2; y2 = C1 (x + C1 /4)

2. The attempt at a solution

I thought that I could take the first equation and set it equal to zero. But the C1 in the second equation is throwing me off.

Am I supposed to set the second equal to C1?

Last edited: Jan 9, 2013
2. Jan 9, 2013

### HallsofIvy

Staff Emeritus
Are you saying that you want to show that $y= \pm\sqrt{C_1(x+ \frac{C_1}{4})}$ satisfies [/itex]y= 2xy'+ y(y')^2[/itex]?

Just find the derivative of y and plug it into the equation.

3. Jan 9, 2013

### aaronfue

Sorry the second equation is y2, but I think I see what you are saying.

4. Jan 9, 2013

### HallsofIvy

Staff Emeritus
Yes, that's why I took the square root to get y.