Q. 135.0( 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





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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