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CBSE Class 12 · 2019 · Differential EquationsLong Answer

Solve the differential equation

\frac{d y}{d x} = - [\frac{x + y cos x}{1 + sin x}]

.

Answer: $y (1 + sin x) = - \frac{x ^{2}}{2} + C$

Solution

Rewrite in linear form:

\frac{d y}{d x} + \frac{cos x}{1 + sin x} y = - \frac{x}{1 + sin x}

I.F. = e^{\int \frac{c o s x}{1 + s i n x} d x} = 1 + sin x

y (1 + sin x) = \int - x d x = - \frac{x ^{2}}{2} + C

y (1 + sin x) = - \frac{x ^{2}}{2} + C

CBSE Class 12 Board · 2019 · Subjective

Practise more: all CBSE board PYQs on Differential Equations →

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