If y=A e^ 5 x +B e^ -5 x , then d^ 2 y d x^ 2 is equal to - Vidyadip

MCQ

If $y=A e^{5 x}+B e^{-5 x}$, then $\frac{d^{2} y}{d x^{2}}$ is equal to

A
-25 y
B
15 y
C
5 y
D
25 y

✓

Answer

(D) 25 y
Explanation: We have,
$y=a e^{5 x}+b e^{-5 x}$
On differentiating w.r.t x, we get
$\frac{d^{2} y}{d x^{2}}=5 \mathrm{ae}^{5 \mathrm{x}}-5 \mathrm{be}^{-5 \mathrm{x}}$
$\frac{d^{2} y}{d x^{2}}=25\left(\mathrm{ae}^{5 \mathrm{x}}+\mathrm{be}^{-5 \mathrm{x}}\right)$
$\frac{d^{2} y}{d x^{2}}=25 \mathrm{y}$
Hence, this is the answer.

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