The degree of the differential equation obtai | vedclass

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(A) Step $1$: Given equation is $(y - a)^2 = 4(x - b)$.Step $2$: Differentiate with respect to $x$: $2(y - a) \frac{dy}{dx} = 4$, which simplifies to

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$1$

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(A) Step $1$: Given equation is $(y - a)^2 = 4(x - b)$.Step $2$: Differentiate with respect to $x$: $2(y - a) \frac{dy}{dx} = 4$, which simplifies to $(y - a) \frac{dy}{dx} = 2$.Step $3$: Differentiate again with respect to $x$: $(y - a) \frac{d^2y}{dx^2} + (\frac{dy}{dx})^2 = 0$.Step $4$: From Step $2$, $y - a = \frac{2}{dy/dx}$. Substitute this into the equation from Step $3$: $\frac{2}{dy/dx} \cdot \frac{d^2y}{dx^2} + (\frac{dy}{dx})^2 = 0$.Step $5$: Multiply by $\frac{dy}{dx}$ to clear the denominator: $2 \frac{d^2y}{dx^2} + (\frac{dy}{dx})^3 = 0$.Step $6$: The highest order derivative is $\frac{d^2y}{dx^2}$, which has an exponent of $1$. Thus, the degree is $1$.

The degree of the differential equation obtained from the equation $(y - a)^2 = 4(x - b)$ [where $a$ and $b$ are arbitrary constants] is

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