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

= e^logx

= x

Solution of the equation is given by

y(I.F) = ∫Q.(I.F)dx + c

⇒ yx = ∫e^x xdx + c

⇒ yx = x∫e^x dx– ∫ ( ∫e^x dx)dx) + c

using integration by part

yx = xe^x–∫e^x dx + c

⇒ yx = xe^x–e^x + c

⇒ yx = (x–1)e^x + c