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Question
Form the differential equation from the following primitive where constants are arbitrary:
xy = a2
Solution
The equation of family of curves is \[xy = a^2\] ...(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
\[y + x\frac{dy}{dx} = 0\]
It is the required differential equation.
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