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


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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