Simple differential equation

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Homework Help Overview

The discussion revolves around solving a differential equation of the form (y')² + x³y' - 2x²y = 0. Participants are exploring potential methods for addressing this equation.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Some participants express difficulty in finding a solution and request hints. Others question the correctness of the provided differential equation, suggesting alternative forms that might be easier to solve. There is also mention of trying specific solution forms, such as y = a x^b.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the equation and considering various approaches. Some guidance has been offered regarding potential forms of solutions, but no consensus has been reached.

Contextual Notes

Participants are working under the constraints of the homework context, which may limit the information provided or the methods discussed. There is uncertainty regarding the original equation's accuracy, which affects the direction of the discussion.

seto6
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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.!
 
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Some misleading title you have there: "simple differential equation..." :)
 
seto6 said:

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' + 2xy1/2)(y - xy1/2) = 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.
 
I seem to find a solution of the form y = a xb, so try that. There's another of the form y = m xn + k too.
 
Last edited:

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