Q. 18

Mark the correct alternative in each of the following:

Solution of the differential equation is

A. x (y + cos x)= sin x + C

B. x (y – cos x)= sin x + C

C. x (y + cos x)= cos x + C

D. none of these

Answer :


Since it is a form of linear differential equation.



Integrating Factor (I.F) = e∫ p dx



Solution of differential equation is given by


y.(I.F) = ∫ Q.(I.F) dx + C


y. x = ∫ (sin x).x dx + C


y. x = ∫ (sin x).x dx + C


Consider integral ∫ (sin x).x dx


Treating x as first function and sin x as second function. So, integrating by Parts we get,


x. (-cos x) + ∫ 1.cos x dx + C


x. cos x + sin x + C


y. x = x. cos x + sin x + C


x (y + cos x) = sin x + C = (A) is the required solution.

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