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CBSE Class 12 · 2006 · Differential EquationsLong Answer

Form the differential equation representing the family of curves

y = a sin (x + b)

, where

a

and

b

are arbitrary constants.

Answer: $\frac{d ^{2} y}{d x ^{2}} + y = 0$

Solution

Two constants

(a, b)

, so differentiate twice.

y^{'} = a cos (x + b), y^{''} = - a sin (x + b) = - y

Hence

\frac{d ^{2} y}{d x ^{2}} + y = 0

CBSE Class 12 Board · 2006 · Subjective

Practise more: all CBSE board PYQs on Differential Equations →

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