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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