Q. 75.0( 1 Vote )

Solve the following differential equations :

Answer :


(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

, 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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