Question

Solve DE: csc(y)dx=sec^2(x)dy

Answer 1

\[\frac{1}{\sin(y)}dx=\frac{1}{\cos^2(x)}dy\]

Answer 2

\[\cos^2(x)dx=\sin(y)dy\] i'm guessing double angle theorem?

Answer 3

the right side is pretty simple

Answer 4

\[\int\limits_{}{}\sin(y)dy=-\cos(y)+c_1\]

Answer 5

going to have to refresh myself on double angles

Answer 6

\[\int\limits_{}{}\cos^2(x)=\int\limits{}{}\frac{1+\cos(2x)}{2}=\frac{1}{2}\int\limits{}{}dx+\frac{1}{2}\int\limits{}{}\cos(2x)dx\]

Answer 7

\[=\frac{1}{2}x+\frac{1}{4}\sin(2x)+c_2\]

Answer 8

other than forgetting a negative

-(-cos(y)=cos(y) it's right =]