If the order and degree of the differential e | vedclass

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(C) Given the family of curves: $y^2=4a(x+a)$ Step $1$: Differentiate with respect to $x$: $2y \frac{dy}{dx} = 4a$ $\implies a = \frac{y}{2} \frac{dy}

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$5$

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(C) Given the family of curves: $y^2=4a(x+a)$ Step $1$: Differentiate with respect to $x$: $2y \frac{dy}{dx} = 4a$ $\implies a = \frac{y}{2} \frac{dy}{dx}$ Step $2$: Substitute the value of $a$ back into the original equation: $y^2 = 4 \left( \frac{y}{2} \frac{dy}{dx} \right) \left( x + \frac{y}{2} \frac{dy}{dx} \right)$ $y^2 = 2y \frac{dy}{dx} \left( x + \frac{y}{2} \frac{dy}{dx} \right)$ $y^2 = 2xy \frac{dy}{dx} + y^2 \left( \frac{dy}{dx} \right)^2$ Step $3$: Identify the order and degree: The highest order derivative is $\frac{dy}{dx}$, so the order $m = 1$. The highest power of the highest order derivative is $2$, so the degree $n = 2$. Step $4$: Calculate $m+n^2$: $m+n^2 = 1 + 2^2 = 1 + 4 = 5$.

If the order and degree of the differential equation corresponding to the family of curves $y^2=4a(x+a)$ (where $a$ is a parameter) are $m$ and $n$ respectively, then $m+n^2=$

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