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CBSE Class 12 · 2018 · Differential EquationsLong Answer

Find the particular solution of the differential equation

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

, given that

y = 0

when

x = \frac{π}{3}

.

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

Solution

Linear with

I.F. = e^{\int 2 t a n x d 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

Apply

y = 0

at

x = \frac{π}{3}

:

0 = sec \frac{π}{3} + C = 2 + C \Rightarrow C = - 2

. Hence

y sec^{2} x = sec x - 2 \Rightarrow y = cos x - 2 cos^{2} x

CBSE Class 12 Board · 2018 · Subjective

Practise more: all CBSE board PYQs on Differential Equations →

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