Differential Equations Question 120
Question: The differential equation of all parabolas whose axes are parallel to 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 $
Show Answer
Answer:
Correct Answer: A
Solution:
The equation of a member of the family of parabolas having axis parallel to y-axis is $ y=Ax^{2}+Bx+C $ …..(i) where A, B, C are arbitrary constants. Differentiating (i) w.r.t. x, we get $ \frac{dy}{dx}=2Ax+B $ …..(ii) Which on differentiating w.r.t. x gives $ \frac{d^{2}y}{dx^{2}}=2A $ …..(iii) Differentiating w.r.t. x again, we get $ \frac{d^{3}y}{dx^{3}}=0 $ .
BETA
