Verify that y = A cos x - b sin x is a solution of the differenti… - Vidyadip

Question

Verify that y = A cos x - b sin x is a solution of the differential equation.
$\frac{\text{d}^{2} \text{y}}{\text{dx}^{2}}+\text{y}=0.$

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Answer

$\frac{\text{dy}}{\text{dx}}=-\text{A sin x - B cos x}$
$\therefore\frac{\text{d}^{2}\text{y}}{\text{dx}^{2}} =-\text{A cos x + B sin x}$
$\therefore\frac{\text{d}^{2}\text{y}}{\text{dx}^{2}}=-\text{(A cos x - B sin x})=-\text{y }\text{ }\therefore\text{ }\frac{\text{d}^{2}\text{y}}{\text{dx}^{2}}+\text{y}=0$
$\therefore$ y = A cos x - B sin x is the solution of given diffential equation.

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