Question

Solve the given differential equation by separation of variables
csc(y) dx + sec^2(x) dy = 0
Please show work

Answer 1

Separating the variables is not so hard:\[\csc ydx+\sec^2xdy=0 \Leftrightarrow \csc ydx=-\sec^2dy\]So\[\frac{ \csc y }{ dy }=-\frac{ \sec^2x }{ dx }\]Now integrate:\[\int\limits_{}^{}\frac{ \csc y }{ dy }=-\int\limits_{}^{}\frac{ \sec^2x }{ dx }\]Have a go at this yourself...(if you want more help, just ask!)

Answer 2

This is just fine.
thank you!

Answer 3

YW!