The solution of the equation d^2 y d x^2 = e^ - 2x is - Vidyadip

MCQ

The solution of the equation $\frac{{{d^2}y}}{{d{x^2}}} = {e^{ - 2x}}$ is

A
$\frac{1}{4}{e^{ - 2x}}$
✓
$\frac{1}{4}{e^{ - 2x}} + cx + d$
C
$\frac{1}{4}{e^{ - 2x}} + c{x^2} + d$
D
$\frac{1}{4}{e^{ - 2x}} + c + d$

✓

Answer

Correct option: B.

$\frac{1}{4}{e^{ - 2x}} + cx + d$

b
(b) $\frac{{{d^2}y}}{{d{x^2}}} = {e^{ - 2x}}$

Integrating both sides, we get $\frac{{dy}}{{dx}} = \frac{{{e^{ - 2x}}}}{{ - 2}} + c$

Again integrate, we get $y = \frac{{{e^{ - 2x}}}}{4} + cx + d$.

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