Q. 425.0( 2 Votes )

Solve the following differential equation

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,




We have



Hence, the solution of the differential equation is,





Let cot–1y = t


[Differentiating both sides]



By substituting this in the above integral, we get




Recall





xet = –{tet – et} + c


xet = –tet + et + c


xet × e–t = (–tet + et + c)e–t


x = –t + 1 + ce–t


[ t = cot–1y]


Thus, the solution of the given differential equation is


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