Simple differential equation

[seto6]

Homework Statement

solve the following differential equation
(y')² +x³y'-2x²y=0

Homework Equations

non

The Attempt at a Solution

i can't seem to find any way to solve it...
could someone give me a hint pls.!

 

[gomunkul51]

Some misleading title you have there: "simple differential equation..." :)

 

[Mark44]

Homework Statement

solve the following differential equation
(y')² +x³y'-2x²y=0

Homework Equations

non

The Attempt at a Solution

i can't seem to find any way to solve it...
could someone give me a hint pls.!

You're sure that you have given us the correct differential equation, right?

If it were y'² + xy' - 2x²y = 0, you could factor it into (y' + 2xy^1/2)(y - xy^1/2) = 0, and you could solve each one separately.

Or if you had y'² + x³y' + 2x²y = 0, you could write this as y'² + d/dx(x³y) = 0. I'm not sure what you could do with that, though.

 

[fzero]

I seem to find a solution of the form y = a x^b, so try that. There's another of the form y = m xⁿ + k too.