Originally Posted by

**yellowrose** Hello,

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))

Mr F says: $\displaystyle \Rightarrow \sin y \, dy = \cos^2 x \, dx \Rightarrow \int \sin y \, dy = \int \cos^2 x \, dx$.

Note that from the double angle formula $\displaystyle \cos (2x) = 2 \cos^2 x - 1$, $\displaystyle \cos^2 x = \frac{1}{2} (\cos(2x) + 1)$.

This will all lead to [snip]4cos(y)=2x+sin(2x)+c

[snip]