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Question
Solve the D.E. 3ex tan y dx + (1 + ex) sec2y dy = 0.
Sum
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Solution
`(3e^x tan y)/(1 + e^x) dx + sec^2y dy = 0`
`(3e^x)/(1 + e^x) dx + (sec^2y)/(tany) dy = 0`
`3 int e^x/(1 + e^x) dx + int (sec^2y)/(tany) dy = 0`
`int (f^'(x))/(fx) dx = log [f(x)]`
3 log (1 + ex) + log (tan y) = log C
log (1 + ex)3 + log (tan y) = log C
log (1 + ex)3 + log tan y = log C
log [(1 + ex)3 · tan y] = log C
log [(1 + ex)3 · tan y] = e log C
(1 + ex)3 · tan y = log C
(1 + ex)3 tan y = C
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