If frac{d^2y}{dx^2} + sin x = 0,then the solu | vedclass

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Question

(A) Given the differential equation: $\frac{d^2y}{dx^2} + \sin x = 0$. Rearranging the terms,we get: $\frac{d^2y}{dx^2} = -\sin x$. Integrating both s

Vedclass · Accepted Answer

$\sin x + c_1x + c_2$

Vedclass · Answer

(A) Given the differential equation: $\frac{d^2y}{dx^2} + \sin x = 0$. Rearranging the terms,we get: $\frac{d^2y}{dx^2} = -\sin x$. Integrating both sides with respect to $x$: $\int \frac{d^2y}{dx^2} dx = \int -\sin x dx$. This gives: $\frac{dy}{dx} = \cos x + c_1$. Integrating again with respect to $x$: $\int \frac{dy}{dx} dx = \int (\cos x + c_1) dx$. Thus,the final solution is: $y = \sin x + c_1x + c_2$.

If $\frac{d^2y}{dx^2} + \sin x = 0$,then the solution of the differential equation is:

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