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## anonymous 3 years ago Solve the diff equation. dr/dø +r*tan(ø)= sec(ø)

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1. anonymous

I just got. r^2/2 + r = tan(ø) + c

2. .Sam.

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

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