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  • Provide solution for RD Sharma maths class 12 chapter 21 Differential Equation exercise Fill in the blank question 10

Provide solution for RD Sharma maths class 12 chapter 21 Differential Equation exercise Fill in the blank question 10

Answers (1)

Answer:

 2

Hint:

 Differentiating w.r.t to ‘x’

Given:

 The family of ellipses having foci on x-axis and center at the origin, is given by

\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1

Solution:

Differentiating w.r.t ‘x’, we get

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

Again by differentiating w.r.t ‘x’ we get

\begin{aligned} &\frac{x\left [ y\frac{\mathrm{d} ^{2}y}{\mathrm{d} x^{2}}+\left ( \frac{\mathrm{d} y}{\mathrm{d} x} \right )^{2} \right ]-\left ( y.\frac{\mathrm{d} y}{\mathrm{d} x} \right )}{x^{2}}=0 \end{aligned}

The required equation is

\begin{aligned} &xy\frac{\mathrm{d} ^{2}y}{\mathrm{d} x^{2}}+x\left ( \frac{\mathrm{d} y}{\mathrm{d} x} \right )^{2}-y.\frac{\mathrm{d} y}{\mathrm{d} x} \qquad \qquad \dots(i) \end{aligned}

∴ Order of the differential equation is the highest derivative present in the differential equation(i)

\begin{aligned} &\frac{\mathrm{d} ^{2}y}{\mathrm{d} x^{2}}=2 \end{aligned}

So, the answer is 2

Posted by

Gurleen Kaur

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