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CBSE Class 12 · 2019 · Differential EquationsLong Answer

Find the differential equation of the family of curves

y = A e^{2 x} + B e^{- 2 x}

, where

A

and

B

are arbitrary constants.

Answer: $\frac{d ^{2} y}{d x ^{2}} - 4 y = 0$

Solution

Two constants

(A, B)

, differentiate twice.

y^{'} = 2 A e^{2 x} - 2 B e^{- 2 x}, y^{''} = 4 A e^{2 x} + 4 B e^{- 2 x} = 4 (A e^{2 x} + B e^{- 2 x}) = 4 y

\frac{d ^{2} y}{d x ^{2}} - 4 y = 0

CBSE Class 12 Board · 2019 · Subjective

Practise more: all CBSE board PYQs on Differential Equations →

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