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Need Solution for R.D.Sharma Maths Class 12 Chapter 21 Differential Equations Exercise Revision Exercise Question 16 Maths Textbook Solution.

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Answer: \frac{d^{3}y}{dx^{3}}=0

Hint: You must know about the equation of all parabola

Given:  equation of all parabolas which have their axes parallel to y-axis is \frac{d^{3}y}{dx^{3}}=0

Solution: Equation of the family of parabolas having axis parallel to y-axis is given by

 \left ( x-n \right )^{2}=4b\left ( y-k \right )..where n,k are constants

Differentiating w.r.t to x,2\left ( x-n \right )=4b\frac{dy}{dx}

\left ( x-n \right )=2b\frac{dy}{dx}

Differentiating again,  1=2b\left ( \frac{d^{2}y}{dx^{2}} \right )

Again Differentiating, 0=2b\left ( \frac{d^{3}y}{dx^{3}} \right )


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