Solve for y explicitly:
dy/dx = 2y/x - (x^2)(y^2)
Show the most crucial steps please.

Question

anonymous · Answer

this is a nonlinear difference equation right?

anonymous · Answer

do you have any boundary conditions that way you can use taylor series expansion

anonymous · Answer

It's a Bernoulli equation which you convert to a linear equation and then solve it.

anonymous · Answer

hmm for final answer in terms of y and x 

$$\frac{1}{3}* \ln (\frac{y^3 - x^3}{x^3}) -lnx +C=0$$

anonymous · Answer

No, the correct answer is: y = 2 / (Cx - x^3)
You treated the equation as a homogenous one, it doesnt look like you can do that.
I solved it by bernoulli and linear solution.

anonymous · Answer

Okay hmm my bad idk about bernoulli method though

anonymous · Answer

Bernoulli are differentialequations on the form: dy/dx + P(x)y = Q(x)y^n
Where n > 1or else it's just a linear equation. You solve it by dividing the equation by y^n, substituting v = y^1-n, and then solve it linearly.