If y = 2 sin 2x - 5 cos 2x, then d^2y/dx^2 + ky = 0. What is k?

Derivatives & Second-Order Derivatives · Question 89 of 96

Question 89

MediumOriginal question

If $y = 2 \sin 2x - 5 \cos 2x$ , then $\frac{d^2y}{dx^2} + ky = 0$ . What is $k$ ?

-4

Correct answerYour answer

4

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5

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8

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Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

Differentiating twice, each term picks up the factor $-4$ : $\frac{d^2y}{dx^2} = - 8 \sin 2x + 20 \cos 2x$ .
That is $-4y$ , so $\frac{d^2y}{dx^2} + 4y = 0$ and $k = 4$ .

Worth noting

$-4$ 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.