Q. 185.0( 2 Votes )

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






given:-



This is a linear differential equation, comparing it with



P = cotx, Q = x2 cotx + 2x


I.F = e∫Pdx


= e∫cotxdx


= elog|sinx|


= sinx


Solution of the equation is given by


y(I.F) = ∫Q.(I.F)dx + c


ysinx = ∫(x2 cosx + 2xsinx)dx + c


ysinx = ∫(x2 cosxdx + ∫2xsinxdx + c


ysinx = x2sinx + c


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