Q. 36 H5.0( 2 Votes )

# Find one-parameter families of solution curves of the following differential equations:

Answer :

Given

This is a first order linear differential equation of the form

Here, P = –1 and Q = y

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

We have

I.F = e–y

Hence, the solution of the differential equation is,

Recall

xe–y = –ye–y – e–y + c

xe–y = –e–y(y + 1) + c

xe–y × ey = [–e–y(y + 1) + c] × ey

x = –(y + 1) + cey

Thus, the solution of the given differential equation is x = –(y + 1) + cey

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