Q. 36 J5.0( 1 Vote )

# Find one-parameter families of solution curves of the following differential equations:e–ysec2ydy = dx + xdy

Answer :

e–ysec2ydy = dx + xdy

Given e–ysec2ydy = dx + xdy

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,

Recall

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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