I am having trouble solving the 2 following problems.
Given the differential equation solve by separation of variables.
1. sec^2(x) dy + csc(y) dx =0
I have tried to get the y's on the left and the x's on the right and integrate, but I cannot get the correct solution. This is what I have so far....
1/(csc(y)) dy = 1/(sec^2(x))
But I'm just not getting 4cos(y)=2x+sin(2x)+c
2. dy/dx = (xy + 3x - y-3) / (xy - 2x + 4y -8)
On this problem I am not sure where to start.
Any help is greatly appreciated. Thanks!
Exponentiate both sides, and let :
which is the same as you book's answer (except that your book did a very bad thing and either forgot to include the arbitrary constant of integration or conveniently set A = 1).
I could guess what mistake you made, but I'll bet that the mistake is obvious in hindsight