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  • Need solution for RD Sharma maths class 12 chapter 21 Differential Equation exercise Fill in the blank question 27

Need solution for RD Sharma maths class 12 chapter 21 Differential Equation exercise Fill in the blank question 27

Answers (1)

Answer:

 Order = 2 or 2nd order

Given:

The order of differential equation representing all circles of radius r is ____

Hint:

 Here, Order = Highest derivative

Solution:

Any circle with given radius can be written as (x-h)2+(y-k)2=r2

Where (h, k) be the Centre of the circle and radius is constant.

Differentiating both side w.r.t x we get

\begin{aligned} &2(x-h)+2(y-k)\frac{\mathrm{d} y}{\mathrm{d} x}=0 \\ &\Rightarrow 2(y-k)\frac{\mathrm{d} y}{\mathrm{d} x}=-2(x-h) \\ &\Rightarrow (y-k)\frac{\mathrm{d} y}{\mathrm{d} x}=-(x-h) \\ &\Rightarrow y\frac{\mathrm{d} }{\mathrm{d} x}\left ( \frac{\mathrm{d} y}{\mathrm{d} x} \right )+\left ( \frac{\mathrm{d} y}{\mathrm{d} x} \right )^{2}=-1 \\ &\Rightarrow \frac{\mathrm{d} ^{2}y}{\mathrm{d} x^{2}}+\left ( \frac{\mathrm{d} y}{\mathrm{d} x} \right )^{2}=-\frac{1}{y} \end{aligned}

Hence order of differential equation will be ‘2’ i.e. 2nd order.

So, the answer is ‘2’ or 2nd order.

Posted by

Gurleen Kaur

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