If y=2 +3 Prove that d^2y dx^2 +y=0 - Vidyadip

Question

If $\text{y}=2\sin\text{x}+3\cos\text{x}$ Prove that $\frac{\text{d}^2\text{y}}{\text{dx}^2}+\text{y}=0$

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Answer

$\text{y}=2\sin\text{x}+3\cos\text{x}$Differentiating w.r.t.x, we get
$\Rightarrow\frac{\text{dy}}{\text{dx}}=2\cos\text{x}+3(-\sin\text{x})=2\cos\text{x}-3\sin\text{x}$
Differentiating w.r.t.x, we get
$\Rightarrow\frac{\text{d}^2\text{y}}{\text{dx}^2}=2(-\sin\text{x})-3\cos\text{x}=-(2\sin\text{x}+3\cos\text{x})=\text{y}$
$\Rightarrow\frac{\text{d}^2\text{y}} {\text{dx}^2}+\text{y}=0$

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