Form the differential equation from the following primitives wher… - Vidyadip

Question

Form the differential equation from the following primitives where constants are arbitrart:

$\text{xy}=\text{a}^2$

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Answer

The equation of family of curves is
$\text{xy}=\text{a}^2\ ...(1)$
where a is an arbitrary constant.
This equation contains only one arbitrary constant, so we shall get a differential equation of first order.
Differentiating equation (1) with respect to x, we get
$\text{y}+\text{x}\frac{\text{dy}}{\text{dx}}=0$
It is the required differential equation.

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