Which of these differential equations has order 2 and degree 1?

\left(\frac{dy}{dx}\right)^2 + y = 0

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\left(\frac{d^2y}{dx^2}\right)^2 + \frac{dy}{dx} = 0

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\frac{d^3y}{dx^3} + y = 0

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\frac{d^2y}{dx^2} + y = 0

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CorrectNot quiteAnswer D

Correct answer: D

Order 2 needs $\frac{d^2y}{dx^2}$ as the highest derivative; degree 1 needs it to the power 1.
Only $\frac{d^2y}{dx^2} + y = 0$ has both. The others have order 1 and degree 2, order 2 and degree 2, and order 3.

Worth noting

$\left(\frac{dy}{dx}\right)^2 + y = 0$ swaps the two: order 1, degree 2.

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Explanation