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Need solution for RD Sharma maths class 12 chapter Differential Equation exercise 21.2 question 12

Answers (1)

Answer:

 2a\frac{\mathrm{d} ^{2}y}{\mathrm{d} x^{2}}+\left ( \frac{\mathrm{d} y}{\mathrm{d} x} \right )^{3}=0

Hint:

 Let the equation of parabola be

(y-k)^{2}=4a(x-h)

 Where h, k are parameter

Given:

Latus rectum 4a and axis are parallel to x-axis

Solution:

 Let the equation of parabola be

(y-k)^{2}=4a(x-h)

 Where h, k are parameter

\begin{aligned} &2(y-k)\frac{\mathrm{d} y}{\mathrm{d} x}=4a \\ &(y-k)\frac{\mathrm{d} y}{\mathrm{d} x}=2a \\ &(y-k)\frac{\mathrm{d}^{2} y}{\mathrm{d} x^{2}}+\left ( \frac{\mathrm{d} y}{\mathrm{d} x} \right )^{2}=0 \\ &2a\frac{\mathrm{d}^{2} y}{\mathrm{d} x^{2}}+\left ( \frac{\mathrm{d} y}{\mathrm{d} x} \right )^{3}=0 \end{aligned}

which is the required differential equation.

Posted by

Gurleen Kaur

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