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

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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