Solving y = 2xy' + y(y')² with given solution y² = C₁(x + C₁/4)

Join the discussion
Registration is free. Ask a follow-up in this thread, or start your own.
Sign up Log in
3 replies · 2K views
aaronfue
Messages
118
Reaction score
0

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?
 
Last edited:

Discussion

Physics news on Phys.org
Are you saying that you want to show that [itex]y= \pm\sqrt{C_1(x+ \frac{C_1}{4})}[/itex] satisfies [/itex]y= 2xy'+ y(y')^2[/itex]?

Just find the derivative of y and plug it into the equation.
 
HallsofIvy said:
Are you saying that you want to show that [itex]y= \pm\sqrt{C_1(x+ \frac{C_1}{4})}[/itex] 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.
 
Yes, that's why I took the square root to get y.