Differential Equations Question 96

Question: The differential equation of all the lines in the xy-plane is

Options:

A) $ \frac{dy}{dx}-x=0 $

B) $ \frac{d^{2}y}{dx^{2}}-x\frac{dy}{dx}=0 $

C) $ \frac{d^{2}y}{dx^{2}}=0 $

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

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Answer:

Correct Answer: C

Solution:

The equation of all the lines in xy-plane is given by $ y=mx+c $

Differentiate it twice w.r.t. x, we get $ \frac{d^{2}y}{dx^{2}}=0 $ .