I need help with a Bernoulli equation...Math wizards wanted!

[Random Variable]

(1/x^2)*dy/dx = y + (1/x)*y^(2/3)

dy/dx = x^2*y +x*y^(2/3)
dy/dx - x^2*y = x*y^(2/3)

let u = y^(1-n)
u = y^(1/3)
y = u^3

dy/dx = 3*u^2*du/dx

3*u^2*(du/dx) - x^2*u^3 = x*u^2
du/dx - (1/3)*x^2*u = x/3

P(x) = -(1/3)*x^2

(-1/3)*Integral (x^2)dx = (-1/9)*x^3

Integrating factor = e^((-1/9)*x^3))

d/dx[e^((-1/9)*x^3))*u] = (x/3)*e^((-1/9)*x^3))

e^((-1/9)*x^3))*u = Integral [(1/3)*x*e^((-1/9)*x^3))]dx

(1/3)*x*e^((-1/9)*x^3))dx can't be integrated. Did I do something wrong?

 

[Random Variable]

bimp

 

[Random Variable]

bimp number two

 

[Whitecloak]

Originally posted by: Vespasian
bimp number two

dy/du = 3*u^2*du/dx

is this correct?

dy/du = 3*u^2

dy/dx = dy/du*du/dx = 3*u^2*du/dx

 

[Random Variable]

Originally posted by: whitecloak

Originally posted by: Vespasian
bimp number two

dy/du = 3*u^2*du/dx

is this correct?

dy/du = 3*u^2

dy/dx = dy/du*du/dx = 3*u^2*du/dx

I meant to write "dy/dx."

 

[eLiu]

Actually...it CAN be integrated, but it's REALLY REALLY REALLY nasty. If you have Maple...use it to integrate. I'm too tired & sick to look at ur other computations...so we'll assume they're right.

 

[Random Variable]

Originally posted by: eLiu
Actually...it CAN be integrated, but it's REALLY REALLY REALLY nasty. If you have Maple...use it to integrate. I'm too tired & sick to look at ur other computations...so we'll assume they're right.

It could be integrated if it had limits. But I was more concerned that I did something wrong in an earlier step.