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Question

(A) Given the equation: $y^2 = 8ax + 8a^2$ $(1)$Differentiating with respect to $x$:$2y \frac{dy}{dx} = 8a$$\Rightarrow a = \frac{y}{4} \frac{dy}{dx}$

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$2$

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(A) Given the equation: $y^2 = 8ax + 8a^2$ $(1)$Differentiating with respect to $x$:$2y \frac{dy}{dx} = 8a$$\Rightarrow a = \frac{y}{4} \frac{dy}{dx}$Substituting the value of $a$ into equation $(1)$:$y^2 = 8 \left( \frac{y}{4} \frac{dy}{dx} \right) x + 8 \left( \frac{y}{4} \frac{dy}{dx} \right)^2$$y^2 = 2xy \frac{dy}{dx} + 8 \left( \frac{y^2}{16} \right) \left( \frac{dy}{dx} \right)^2$$y^2 = 2xy \frac{dy}{dx} + \frac{y^2}{2} \left( \frac{dy}{dx} \right)^2$Multiplying by $2$ to clear the fraction:$2y^2 = 4xy \frac{dy}{dx} + y^2 \left( \frac{dy}{dx} \right)^2$In this differential equation,the highest order derivative is $\frac{dy}{dx}$,which has an order of $1$. The highest power of the highest order derivative is $2$. Therefore,the degree is $2$.

The degree of the differential equation whose solution is $y^2=8a(x+a)$ is

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