Which of the following statements are true? I. y = e^3x satisfies d^2y/dx^2 = 9y. II. y = sin 3x satisfies d^2y/dx^2 = 9y. III. y = cos 3x satisfies d^2y/dx^2 + 9y = 0. IV. y = e^-3x satisfies d^2y/dx^2 = -9y.

Question 87

MediumOriginal question

Which of the following statements are true?
I. $y = e^{3x}$ satisfies $\frac{d^2y}{dx^2} = 9y$ .
II. $y = \sin 3x$ satisfies $\frac{d^2y}{dx^2} = 9y$ .
III. $y = \cos 3x$ satisfies $\frac{d^2y}{dx^2} + 9y = 0$ .
IV. $y = e^{-3x}$ satisfies $\frac{d^2y}{dx^2} = -9y$ .

I, II and III onlyCorrect answerYour answerI and III onlyCorrect answerYour answerI, III and IV onlyCorrect answerYour answerII and IV onlyCorrect answerYour answer

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CorrectNot quiteAnswer B

Correct answer: B

Exponentials keep their sign: $e^{3x}$ and $e^{-3x}$ both give $\frac{d^2y}{dx^2} = 9y$ , so I is true and IV is false.
Sine and cosine change sign: both give $\frac{d^2y}{dx^2} = -9y$ , so II is false and III is true.

Concept: Which functions satisfy which relation
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