Differential EquationseasyFree

DE of All Parabolas with Axis Parallel to y-axis | JEE

JEE Maths question with a full step-by-step solution.

Question

The differential equation of all parabolas with axis parallel to the

y

-axis is:

\dfrac{d^2y}{dx^2} = 2y + x

\dfrac{d^3y}{dx^3} = 2y

\left(\dfrac{d^2y}{dx^2}\right)^3 = \dfrac{dy}{dx}

\dfrac{d^3y}{dx^3} = 0

correct

Solution

A parabola with axis parallel to the

y

-axis has the form

x^2 + ax + by + c = 0,

with three arbitrary constants

a, b, c

, so we differentiate three times.

2x + a + b\frac{dy}{dx} = 0

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

b\frac{d^3y}{dx^3} = 0 \Rightarrow \frac{d^3y}{dx^3} = 0.

Correct answer: (4)

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