Ordinary Differential Equations

[aaronfue]

Homework Statement

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?

 

[HallsofIvy]

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.

 

[aaronfue]

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.

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

 

[HallsofIvy]

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