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CBSE Class 12 · 2022 · Differential EquationsLong Answer

Solve the following differential equation:

(y - sin^{2} x) d x + tan x d y = 0

Answer: $y sin x = \frac{sin ^{3} x}{3} + C$

Solution

Rearrange:

tan x \frac{d y}{d x} + y = sin^{2} x

, i.e.

\frac{d y}{d x} + cot x y = \frac{sin ^{2} x}{tan x} = sin x cos x

I.F. = e^{\int c o t x d x} = sin x

y sin x = \int sin x \cdot sin x cos x d x = \int sin^{2} x cos x d x = \frac{sin ^{3} x}{3} + C

y sin x = \frac{sin ^{3} x}{3} + C

CBSE Class 12 Board · 2022 · Subjective

Practise more: all CBSE board PYQs on Differential Equations →

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