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

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

its been a while since I had diff eq and this problem came up, could i get some help please?

2. Re: dy/dx= x / (x^2y+y^3)

What methods do you know on how to solve DEs?

3. Re: dy/dx= x / (x^2y+y^3)

I know i need to separate and integrate, but i cant quite figure out how. I know there is probably some substitution in there but I'm not getting it

4. Re: dy/dx= x / (x^2y+y^3)

Originally Posted by firestar928
dy/dx= x / (x^2y+y^3)

its been a while since I had diff eq and this problem came up, could i get some help please?
Writing the DE in different way, changing the role of x and y, You obtain...

$\frac{d x}{dy} = x\ y + \frac{y^{3}}{x}$ (1)

... which is 'Bernoulli type'. The solving procedure is illustrated in...

Bernoulli Differential Equation -- from Wolfram MathWorld

It is remarkable the fact that a Bernoulli equation has standard form...

$x^{'} + p(y)\ x = q(y)\ x^{n}$ (2)

... and the solving procedure is valid also when n is a negative number like in this case [n=-1...]

Kind regards

$\chi$ $\sigma$

5. Re: dy/dx= x / (x^2y+y^3)

Another way: the equation has an integrating factor $\mu=\mu(y)$ that depends on $y$ .

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(x 2y^3)dy/dx=y

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