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  • Provide Solution For R.D.Sharma Maths Class 12 Chapter 21 Differential Equations Exercise Revision Exercise Question 8 Maths Textbook Solution.

Provide Solution For R.D.Sharma Maths Class 12 Chapter 21 Differential Equations Exercise  Revision Exercise Question 8 Maths Textbook Solution.

Answers (1)

Answer:

                xy{}'-2y=0

Hint:

You must know about the parabolas to form an equation

Given:

Family of parabola having vertex at origin and axis along the positive y-direction

Solution:

x^{2}=4ay                                                                                                                                                           … (i)

Where, a is constant parameter

Differentiate with respect to x,

\begin{aligned} &2 x=4 a \frac{d y}{d x} \\ &x=2 a y^{\prime} \\ &a=\frac{x}{2 y^{\prime}} \\ &\text { Put in (i) } \\ &x^{2}=4 \frac{x}{2 y^{\prime}} \cdot y \\ &y^{\prime}=\frac{2 y}{x} \\ &x y^{\prime}=2 y \\ &x y^{\prime}-2 y=0 \end{aligned}

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