The solution of the equation frac{d^2y}{dx^2} | vedclass

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Question

(B) Given the differential equation: $\frac{d^2y}{dx^2} = e^{-2x}$.Integrating both sides with respect to $x$ once:$\int \frac{d^2y}{dx^2} dx = \int e

Vedclass · Accepted Answer

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

Vedclass · Answer

(B) Given the differential equation: $\frac{d^2y}{dx^2} = e^{-2x}$.Integrating both sides with respect to $x$ once:$\int \frac{d^2y}{dx^2} dx = \int e^{-2x} dx$$\frac{dy}{dx} = \frac{e^{-2x}}{-2} + c = -\frac{1}{2}e^{-2x} + c$.Integrating both sides with respect to $x$ again:$\int \frac{dy}{dx} dx = \int (-\frac{1}{2}e^{-2x} + c) dx$$y = -\frac{1}{2} \cdot \frac{e^{-2x}}{-2} + cx + d$$y = \frac{1}{4}e^{-2x} + cx + d$.Thus,the correct option is $B$.

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

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