Answer :

Formula:-


(i) If a differential equation is ,


then y(I.F) = ∫Q.(I.F)dx + c, where I.F = e∫Pdx


(ii) ∫dx = x + c




Given:-



This is a linear differential equation, comparing it with



, Q =


I.F = e∫Pdx



= elogx


= x


Solution of the equation is given by


y(I.F) = ∫Q.(I.F)dx + c


yx = ∫ex xdx + c


yx = x∫ex dx– ∫ ( ∫ex dx)dx) + c


using integration by part


yx = xex–∫ex dx + c


yx = xex–ex + c


yx = (x–1)ex + c



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