Q. 135.0( 1 Vote )

# Solve the following differential equations :

(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

P = 1, Q = cosx

I.F = e∫Pdx

= e∫dx

= ex

Solution of the equation is given by

y(I.F) = ∫Q.(I.F)dx + c1

y ex = ∫cosx. ex dx + c1

let I = ∫ ex cosxdx

= cosx∫ exdx ∫(sinx∫exdx)dx + c2

using integrating by part

I = ex cosx + ∫sinxexdx + c

= ex cosx [sinx∫exdx∫(cosx∫exdx)dx] + c2

I = ex cosx + sinxex–I + C2

2I = (cosx + sinx)ex + C2

putting I

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