y = a sin x + b cos x is the solution of

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Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Differential Equations

Question:

y = a sin x + b cos x is the solution of differential equation :

Options:

$\frac{d^2 y}{d x^2}+y=0$

$\frac{d y}{d x}+y=0$

$\frac{d^2 y}{d x^2}=y$

$\frac{d y}{d x}=y$

Correct Answer:

$\frac{d^2 y}{d x^2}+y=0$

Explanation:

$\frac{d y}{d x}=a \cos x-b \sin x \Rightarrow \frac{d^2 y}{d x^2}=-a \sin x-b \cos x=-y$

Hence $\frac{d^2 y}{d x^2}+y=0$

Hence (1) is the correct answer.