Q. 275.0( 1 Vote )

# Solve the following differential equations: Given   This is a first order linear differential equation of the form Here, P = –tan x and Q = –2 sin x

The integrating factor (I.F) of this differential equation is,   We have   [ m log a = log am] [ elog x = x]

I.F = cos x

Hence, the solution of the differential equation is,   Let cos x = t

–sinxdx = dt [Differentiating both sides]

By substituting this in the above integral, we get Recall   yt = t2 + c   [ t = cos x]

y = cos x + c sec x

Thus, the solution of the given differential equation is y = cos x + c sec x

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