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Question

The general solution of the differential equation dydx+y cot x = cosec x, is
(a) x + y sin x = C
(b) x + y cos x = C
(c) y + x (sin x + cos x) = C
(d) y sin x = x + C

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Solution

(d) y sin x = x + C


We have,dydx+y cot x=cosec xdydx+ycot x=cosec xComparing with dydx+Py=Q, we getP=cot x Q=cosec xNow, I.F.=ecot x dx=elogsin x =sin xSo, the solution is given byysinx=sin x×cosec x dx+Cy sin x=x +C

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