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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.

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 )

i.e.\frac{d^{3}y}{dx^{3}}=0

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