Question

Find the solution:
ysec^(2) xdx - cot^(3) xln^(2)ydy=0
Y(pi/4) = e

Answer 1

have you tried this?

Answer 2

\[y \sec ^2x~dx=\cot ^3x~\ln^2y~dy\]
divide by \[y \cot ^3x\]
\[\tan ^3x \sec ^2x~dx=\frac{ \ln ^2y~dy }{ y }\]
check the statement?

Answer 3

is it ln y^2?

Answer 4

Either way, a substitution of \(\ln y\) makes integration of the RHS easy.

Answer 5

correct.