Question

I need to make this differential equations with the separation of variables method but I really dont know how to do it, can anybody help me out here and explain step by step what are you doing? thanks so much in advance!
Here are the equations

1) csc y dx + sec^2 x dy = 0

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

Answer 1

just put all that depend on y one side (including dy) and what depends on x other side and integrate

Answer 2

1) sin(y) dy = -cos^2(x) dx

Answer 3

do same in the other one

Answer 4

And then I just need to integrate each side of the equality?

Answer 5

yes

Answer 6

Thank you so much!

Answer 7

welcome

Answer 8

I am having trouble to take the x on one side and the y on the other can anybody help me out with this one? thanks!

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