Question

checks if
y^2 dx + 2xy dy = 0
is an exact differential equations

Answer 1

@ivanmlerner

Answer 2

@jim_thompson5910

Answer 3

what did u get it??

Answer 4

I got xy^2, as the potential function and since it is a continuously differentiable function this is an exact differential equation.

Answer 5

but i got 2y..., can show ur work to me?

Answer 6

I integrated the first function in respect to x and the second in respect to y. For the equation to be an exact diferential equation they need to be equal and continuously differentiable.
I believe you took the derivative instead of integrating, since this equation is defined in all reals, and the reals are a simply connected set, what you did works just as well, and since the derivatives are all 2y you can say that the equation is exact.
In your way you used the condition for the potential function to exist, and with mine I found what the potential function was since it was an easy function to integrate but your way is even better because it is easier to apply in general.

Answer 7

yes.., ok thank u so much @ivanmlerner :)