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CBSE Class 12 · 2008 · Differential EquationsLong Answer

Solve the following differential equation:

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

Answer: $y = tan x - 1 + C e^{- t a n x}$

Solution

Divide by

cos^{2} x

:

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

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

y e^{t a n x} = \int e^{t a n x} tan x sec^{2} x d x

Put

t = tan x

:

\int t e^{t} d t = e^{t} (t - 1)

, so

y e^{t a n x} = e^{t a n x} (tan x - 1) + C \Rightarrow y = tan x - 1 + C e^{- t a n x}

CBSE Class 12 Board · 2008 · Subjective

Practise more: all CBSE board PYQs on Differential Equations →

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