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haganmc

  • 3 years ago

Solve the diff equation. dr/dø +r*tan(ø)= sec(ø)

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  1. haganmc
    • 3 years ago
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    I just got. r^2/2 + r = tan(ø) + c

  2. .Sam.
    • 3 years ago
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    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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