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Order of a Differential Equation

The different...

Question

The differential equation corresponding to $x y = c^{2}$ , where $c$ is an arbitrary constant, is:

x y^{''} + x = 0

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y^{''} = 0

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x y^{'} + y = 0

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x y^{''} - x = 0

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Solution

The correct option is C $x y^{'} + y = 0$
Given equation is $x y = c^{2}$ .

Differentiating w.r.t. $x$ , we get

$x \frac{d y}{d x} + y = 0$

This can be written as $x y^{'} + y = 0$

Hence, option C is correct.

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