Find the general solution of each of the following differential equations:
`3e^(x)tany dx +(1-e^(x))sec^(2)y dy=0`

Answer

`tany = C (1-e^(-x))^(3)`

Explanation

`int (3e^(x))/((1-e^(x)))dx+int(sec^(2)y)/(tany)dy=log|C_(1)|`
`rArr -3int (-e^(x))/((1-e^(x)))dx+int (sec^(2)y)/(tany)dy =log|C_(1)|rArr -3log|1-e^(-x)|+log|tan y|=log|C_(1)|`
`rArr log|(1-e^(-x))^(-3)tany|=log|C_(1)|rArr (tan y)/((1-e^(-x))^(3)) = pm C_(1)=C.`