The order and degree of the differential equa | vedclass

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(A) Step $1$: Simplify the given equation. $\sqrt{\frac{(\frac{dy}{dx})^2 + 1}{(\frac{dy}{dx})^2}} = (\frac{d^2y}{dx^2})^{\frac{3}{2}}$.Step $2$: Squa

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Order $2$, Degree $3$

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(A) Step $1$: Simplify the given equation. $\sqrt{\frac{(\frac{dy}{dx})^2 + 1}{(\frac{dy}{dx})^2}} = (\frac{d^2y}{dx^2})^{\frac{3}{2}}$.Step $2$: Square both sides to remove the square root: $\frac{(\frac{dy}{dx})^2 + 1}{(\frac{dy}{dx})^2} = (\frac{d^2y}{dx^2})^3$.Step $3$: Multiply by $(\frac{dy}{dx})^2$ to clear the fraction: $(\frac{dy}{dx})^2 + 1 = (\frac{d^2y}{dx^2})^3 (\frac{dy}{dx})^2$.Step $4$: The highest order derivative present is $\frac{d^2y}{dx^2}$, so the order is $2$.Step $5$: The power of the highest order derivative after making the equation a polynomial in derivatives is $3$, so the degree is $3$.

The order and degree of the differential equation $\sqrt{1 + \frac{1}{(\frac{dy}{dx})^2}} = (\frac{d^2y}{dx^2})^{\frac{3}{2}}$ are ...

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