The degree of the differential equation obtai | vedclass

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Question

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

Vedclass · Accepted Answer

$1$

Vedclass · Answer

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