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What is the degree and order of the differential equation $$\frac{dy}{dx}=x\sqrt{\frac{dy}{dx}}?$$

On squaring we get $$\left [ \frac{dy}{dx} \right ]^2=x^2\frac{dy}{dx}$$ At this stage order is 1 and degree is 2. But if I cancel the common factor it becomes $$\frac{dy}{dx}=x^2$$ Here the order is 1 and degree is 1 . So which one is its order and degree?

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    $\begingroup$ Order and degree can change when you modify the original DE. For the original equation, the order is one and the degree is one. $\endgroup$
    – Vasili
    Dec 4, 2023 at 14:32
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    $\begingroup$ I would say, because of the square-root, the "degree" is not defined. $\endgroup$
    – GEdgar
    Dec 4, 2023 at 15:21

1 Answer 1

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If you cancel, you are eliminating one solution of the equation, which is dy/dx = 0. So it becomes a different equation.

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