Q. 65.0( 1 Vote )

Solve the following differential equations :


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



This is a linear differential equation, comparing it with



P = 2, Q = 4x


I.F = e∫Pdx


= e∫2dx


= e2x


Solution of the equation is given by


y(I.F) = ∫Q.(I.F)dx + c


y(e2x) = ∫4x.e2x dx + c


y(e2x) = 4(x∫e2x dx– ∫ ( ∫e2x dx)dx) + c


using integration by part







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