Q. 36 G5.0( 1 Vote )

Find one-parameter families of solution curves of the following differential equations:


Answer :


Given



This is a first order linear differential equation of the form



Here, P = cos x and Q = esin x cos x


The integrating factor (I.F) of this differential equation is,



We have


I.F = esin x


Hence, the solution of the differential equation is,






Let sin x = t


cosxdx = dt [Differentiating both sides]


By substituting this in the above integral, we get



Recall





[ t = sin x]


Thus, the solution of the given differential equation is


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