If y = 3 sin x + 4 cos x, then d^2y/dx^2 + ky = 0. What is k?

Derivatives & Second-Order Derivatives · Question 83 of 96

Question 83

EasyOriginal question

If $y = 3 \sin x + 4 \cos x$ , then $\frac{d^2y}{dx^2} + ky = 0$ . What is $k$ ?

-1

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0

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1

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CorrectNot quiteAnswer C

Correct answer: C

Differentiating twice, each term picks up the factor $-1$ : $\frac{d^2y}{dx^2} = - 3 \sin x - 4 \cos x$ .
That is $-1y$ , so $\frac{d^2y}{dx^2} + 1y = 0$ and $k = 1$ .

Worth noting

$-1$ is what $\frac{d^2y}{dx^2}$ equals as a multiple of $y$ ; moving it across the equals sign changes its sign.

Ten questions from Derivatives & Second-Order Derivatives, at your own pace.

Ten questions from Derivatives & Second-Order Derivatives, at your own pace.