Match the following, A, B, C, D
List - I LIST- II
A) The D.E's of $y = A e^{x} + B e^{- x}$ ( $A, B$ arbitrary constants) 1. $y_{2} + m^{2} y = 0$
B) $y = a s i n p x + b c o s p x$ ( $a, b$ arbitrary constants) 2. $y_{3} = 0$
C) $y = a x^{2} + b x + c$ ( $a, b, c$ arbitrary constants) 3. $y_{2} - y = 0$
D) $y = a s i n (m x + b)$ ( $a, b, c$ arbitrary constants) 4. $y_{2} + p^{2} y = 0$
5. $y_{2} - m^{2} y = 0$

5, 2, 3, 4

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2, 3, 4, 5

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4, 3, 2, 1

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3, 4, 2, 1

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Solution

The correct option is D 3, 4, 2, 1
$A) y = {A e}^{x} + {B e}^{- x} \Rightarrow y_{1} = {A e}^{x} - {B e}^{- x} \Rightarrow y_{2} = {A e}^{x} + {B e}^{- x} ∴ y_{2} - y = 0$
$B) y = a sin p x + b cos p x \Rightarrow y_{1} = a p cos p x - b p sin p x \Rightarrow y_{2} = - {a p}^{2} sin p x - b p^{2} cos p x ∴ y_{2} + p^{2} y = 0$

$C) y = {a x}^{2} + b x + c \Rightarrow y_{1} = 2 a x + b \Rightarrow y_{2} = 2 a \Rightarrow y_{3} = 0$

$D) y = a cos (m x + b) \Rightarrow y_{1} = - a m sin (m x + b) \Rightarrow y_{2} = - {a m}^{2} cos (m x + b) ∴ y_{2} + m^{2} y = 0$

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List - I	LIST- II
A) The D.E's of $y = A e^{x} + B e^{- x}$ ( $A, B$ arbitrary constants)	1. $y_{2} + m^{2} y = 0$
B) $y = a s i n p x + b c o s p x$ ( $a, b$ arbitrary constants)	2. $y_{3} = 0$
C) $y = a x^{2} + b x + c$ ( $a, b, c$ arbitrary constants)	3. $y_{2} - y = 0$
D) $y = a s i n (m x + b)$ ( $a, b, c$ arbitrary constants)	4. $y_{2} + p^{2} y = 0$
	5. $y_{2} - m^{2} y = 0$