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CBSE Class 12 · 2006 · Differential EquationsLong Answer

Solve the following differential equation:

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

Answer: $y (sec x + tan x) = sec x + tan x - x + C$

Solution

Linear with

P = sec x

,

Q = tan x

.

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

y (sec x + tan x) = \int tan x (sec x + tan x) d x = \int (sec x tan x + sec^{2} x - 1) d x

= sec x + tan x - x + C

y (sec x + tan x) = sec x + tan x - x + C

CBSE Class 12 Board · 2006 · Subjective

Practise more: all CBSE board PYQs on Differential Equations →

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