The order and degree of the differential equa | vedclass

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Question

(A) Step $1$: Rewrite the equation to remove the fractional exponent: $3 - (\frac{d^3y}{dx^3})^{2/3} = (\frac{dy}{dx})^5 \implies 3 - (\frac{dy}{dx})^

Vedclass · Accepted Answer

$3, 2$

Vedclass · Answer

(A) Step $1$: Rewrite the equation to remove the fractional exponent: $3 - (\frac{d^3y}{dx^3})^{2/3} = (\frac{dy}{dx})^5 \implies 3 - (\frac{dy}{dx})^5 = (\frac{d^3y}{dx^3})^{2/3}$.Step $2$: Cube both sides to eliminate the fractional power: $(3 - (\frac{dy}{dx})^5)^3 = (\frac{d^3y}{dx^3})^2$.Step $3$: The highest order derivative present is $\frac{d^3y}{dx^3}$, so the order is $3$.Step $4$: The power of the highest order derivative after making the equation free from radicals and fractions is $2$, so the degree is $2$.

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

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