Q. 265.0( 2 Votes )

Solve the following differential equations:

dx + xdy = e–ysec2ydy

Answer :

Given dx + xdy = e–ysec2ydy

This is a first order linear differential equation of the form

Here, P = 1 and e–ysec2y

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

We have

I.F = ey [ elog x = x]

Hence, the solution of the differential equation is,


xey = tan y + c

x = (tan y + c)e–y

Thus, the solution of the given differential equation is x = (tan y + c)e–y

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