Q. 37 N5.0( 1 Vote )

Solve each of the following initial value problems:

dy = cos x (2 – y cosec x)dx

Answer :

dy = cos x (2 – y cosec x)dx


Given dy = cos x (2 – y cosec x)dx








This is a first order linear differential equation of the form



Here, P = cot x and Q = 2 cos x


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




We have



I.F = sin x [ elog x = 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




yt = t2 + c




[ t = sin x]


Thus, the solution of the given differential equation is


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