Question

(ODE) Trying to solve a basic Differential Equation, prompt posted below momentarily.

Answer 1

\[\text{Solve the differential equation.}\]\[\frac{x^2}{y^2}\frac{dy}{dx}-\frac{\sqrt{y^2+4}}{x+1}=0\]

Answer 2

@dan815 , should I treat this like a separable equation, probably? Going to take a shot at it like that.

Answer 3

\[\frac{x^2}{y^2}\frac{dy}{dx}=\frac{\sqrt{y^2+4}}{x+1}\]

Answer 4

\[\frac{x^2}{y^2}\frac{dy}{dx}(x+1)=\sqrt{y^2+4}\]

Answer 5

its separable isnt it

Answer 6

\[\frac{dy}{dx}(x^2)(x+1)=\sqrt{y^2+4}y^2\]

Answer 7

(Yeah, heh, I'm just still shaky on this and am basically looking for validation to make absolutely sure I'm headed in the right direction, heh, I really don't want to mess up at the beginning)

Answer 8

its separable so

Answer 9

Alright, but what do I do about this dy/dx business where the differentials would be attached to the wrong side?

Answer 10

Yeah, I am separating it, right?

Answer 11

might have to do some u sub or parts on that sqrt one

Answer 12

But I mean, the differentials would be attached to the wrong side, I think I figured it out