Q. 18

Mark the correct alternative in each of the following:Solution of the differential equation isA. x (y + cos x)= sin x + CB. x (y – cos x)= sin x + CC. x (y + cos x)= cos x + CD. none of these

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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