Transforming a Differential Equation: Tips and Tricks

[discoverer02]

I need to put this general solution to a differential in the following form:

My solution is in the form (-x^3)(y^(-1)) + (x^2)y = C

It needs to be in the form y = (x^(-2))[c+-((c^2) + x^5)^(1/2)]

I've been noodling around with it for a while and it's not working out for me. Does anyone something I can factor out or multiply by that will put it into a friendlier form?

Thanks.

 

[NateTG]

You've got:
$$\frac{-x^3}{y}+x^2y=C$$
$$-x^3=Cy-x^2y^2$$
Which is a quadratic equation in $$y$$.
$$x^2y^2-Cy-x^3=0$$
Apply the quadratic formula, and you should get there.

 

[cookiemonster]

Multiply through by y and you have a quadratic equation in the y variable.

cookiemonster

 

[discoverer02]

Thanks.

I should have seen this. It's a no brainer. Where was my brain last night?[zz)]