Q. 36 E5.0( 1 Vote )

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, and


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




Let t = log x


[Differentiating both sides]


By substituting this in the above integral, we get



We have


I.F = elog t


I.F = t [ elog x = x]


I.F = log x [ t = log x]


Hence, the solution of the differential equation is,





Let t = log x


[Differentiating both sides]


By substituting this in the above integral, we get



We know






[ t = log x]


Thus, the solution of the given differential equation is


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