Q. 255.0( 1 Vote )

# Solve the following differential equations:(x + tan y)dy = sin 2y dx

Given (x + tan y)dy = sin 2y dx

This is a first order linear differential equation of the form

Here, P = –cosec 2y and

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

We have

[ m log a = log am]

[ elog x = x]

Hence, the solution of the differential equation is,

Let tan y = t

sec2y dy = dt [Differentiating both sides]

By substituting this in the above integral, we get

Recall

[ t = tan y]

Thus, the solution of the given differential equation is

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