CBSE Class 12 Math 2020 Delhi Set 1 Solved Paper - Question 3 | ...

CBSE Class 12 Math 2020 Delhi Set 1 Solved Paper

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Question : 3 of 36

Marks: +1, -0

If

{\y}={A {\e } ^ { 5 x }}+ {\Be}^{-5 x}

, then

\;{ {\d}^2 {\y}}/{ {\d} x^2}

is equal to

$25 {\y}$
$5 {\y}$
$-25 y$
$15 {\y}$

Solution:

Given:

y=A e^{5 x}+B e^{-5 x}

∴ \;\;{d y}/{d x}=5 {\A} e^{5 x}-5 {\B} e^{-5 x}

⇒ \;{d^2 y}/{d x^2}=25 {\A} e^{5 x}+25 {\B} e^{-5 x}

⇒ \;{d^2 y}/{d x^2}=25 y .

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