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  • The differential equation for which y=a \cos x+b \sin x is a solution, is (a) frac{d^{2} y}{d x^{2}}+y=0

The differential equation for which y=a \cos x+b \sin x is a solution, is
(a) \frac{d^{2} y}{d x^{2}}+y=0
(b) \frac{d^{2} y}{d x^{2}}-y=0
(c) \frac{d^{2}}{d x^{2}}+(a+b) y=0
(d) \frac{d^{2} y}{d x^{2}}+(a-b) y=0

Answers (1)

The answer is the option (a)  \frac{d^{2} y}{d x^{2}}+y=0$

Explanation: -

On differentiating both sides w.r.t. x, we get \frac{d y}{d x}=-a \sin x+b \cos x$
Again, differentiating w.r.t. x, we get \frac{d^{2} y}{d x^{2}}=-a \cos x-b \sin x$
\\\Rightarrow \quad \frac{d^{2} y}{d x^{2}}=-y$ \\$\Rightarrow \quad \frac{d^{2} y}{d x^{2}}+y=0$

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infoexpert22

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