Differential Equations Question 183
Question: The differential equation of all parabolas whose axis are parallel to the y-axis is
Options:
A) $ \frac{d^{3}y}{dx^{3}}=0 $
B) $ \frac{d^{2}x}{dy^{2}}=C $
C) $ \frac{d^{3}y}{dx^{3}}+\frac{d^{2}x}{dy^{2}}=0 $
D) $ \frac{d^{2}y}{dx^{2}}+2\frac{dy}{dx}=C $
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Answer:
Correct Answer: A
Solution:
[a] The equation of a member of the family of parabolas having axis parallel to y-axis is $ y=Ax^{2}+Bx+C $
…(1) Where A, B, and C are arbitrary constants. Differentiating equation (1) w.r.t. x, we get $ \frac{dy}{dx}=2Ax+B $
…(2) Which on again differentiating w.r.t. x gives $ \frac{d^{2}y}{dx^{2}}=2A $
…(3) Differentiating (3) w.r.t. x, we get $ \frac{d^{3}y}{dx^{3}}=0 $
BETA
