The order and degree of the differential equa | vedclass

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Question

(B) Step $1$: Given the differential equation $\sqrt{2 + (\frac{d^2y}{dx^2})^3} = (\frac{d^3y}{dx^3})^{5/2}$.Step $2$: Square both sides to remove the

Vedclass · Accepted Answer

$3, 5$

Vedclass · Answer

(B) Step $1$: Given the differential equation $\sqrt{2 + (\frac{d^2y}{dx^2})^3} = (\frac{d^3y}{dx^3})^{5/2}$.Step $2$: Square both sides to remove the square root: $2 + (\frac{d^2y}{dx^2})^3 = (\frac{d^3y}{dx^3})^5$.Step $3$: The order of a differential equation is the highest derivative present. Here, the highest derivative is $\frac{d^3y}{dx^3}$, so the order is $3$.Step $4$: The degree is the power of the highest derivative when the equation is expressed as a polynomial in derivatives. The power of $\frac{d^3y}{dx^3}$ is $5$. Thus, the degree is $5$.

The order and degree of the differential equation $\sqrt{2 + (\frac{d^2y}{dx^2})^3} = (\frac{d^3y}{dx^3})^{5/2}$ are respectively:

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