Differential equations question

[nocloud]

i have this equation:
dx/dt = t/(x*t^2+x^3)

using the substitution u = t^2, i obtain the following equation:

du/dx = 2u/(ux+x^3)

does anybody know how i can solve this equation?

 

[HallsofIvy]

i have this equation:
dx/dt = t/(x*t^2+x^3)

using the substitution u = t^2, i obtain the following equation:

du/dx = 2u/(ux+x^3)

does anybody know how i can solve this equation?

No, you don't obtain that equation. If u= t^2, then dx/dt= dx/du du/dt=2t dx/du.
The equation becomes 2t dx/du= t/(xu+ x^3) or dx/du= 1/(2(xu+x^3). Then
du/dx= 2(xu+ x^3). Unfortunately, since we still cannot separate u and x, that doesn't really help.

 

[nocloud]

ah, my bad,

okay, this problem is now very easy then since its linear and i can just use an integrating factor