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CBSE Class 12 · 2006 · Differential EquationsLong Answer

Solve the following differential equation:

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

Answer: $y sec^{2} x = sec x + C$ (i.e. $y = cos x + C cos^{2} x$ )

Solution

Linear with

P = 2 tan x

.

I.F. = e^{\int 2 t a n x d x} = e^{2 l o g ∣ s e c x ∣} = sec^{2} x

y sec^{2} x = \int sin x sec^{2} x d x = \int sec x tan x d x = sec x + C

y sec^{2} x = sec x + C \Rightarrow y = cos x + C cos^{2} x

CBSE Class 12 Board · 2006 · Subjective

Practise more: all CBSE board PYQs on Differential Equations →

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