Question

Solve the diff equation.

dr/dø +r*tan(ø)= sec(ø)

Answer 1

I just got.

r^2/2 + r = tan(ø) + c

Answer 2

try let\[\lambda (ø)\text{ = }\exp (\int\limits \tan (ø) \, dø)\text{ = }\sec (ø)\]
then
\[(\sec (ø) \tan (ø)) r(ø)+\sec (ø) \frac{dr(ø)}{dø}\text{ = }\sec ^2(ø)\]
\[substitute, ~~\sec (ø) \tan (ø)\text{ = }\frac{d\sec (ø)}{dø}\]
\[\frac{d\sec (ø)}{dø} r(ø) +\sec (ø) \frac{dr(ø)}{dø}\text{ = }\sec ^2(ø)\]
then use reverse product rule see if it works