The order and degree of the differential equa | vedclass

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Question

(A) Step $1$: Rewrite the equation to eliminate the fractional exponent: $3 - (\frac{d^3y}{dx^3})^{7/3} = (\frac{dy}{dx})^5 \implies 3 - (\frac{dy}{dx

Vedclass · Accepted Answer

$3, 7$

Vedclass · Answer

(A) Step $1$: Rewrite the equation to eliminate the fractional exponent: $3 - (\frac{d^3y}{dx^3})^{7/3} = (\frac{dy}{dx})^5 \implies 3 - (\frac{dy}{dx})^5 = (\frac{d^3y}{dx^3})^{7/3}$.Step $2$: Cube both sides to remove the fractional power $1/3$: $(3 - (\frac{dy}{dx})^5)^3 = (\frac{d^3y}{dx^3})^7$.Step $3$: The order is the highest derivative present, which is $3$. The degree is the power of the highest derivative after making the equation a polynomial in derivatives, which is $7$.Step $4$: Thus, the order is $3$ and the degree is $7$.

The order and degree of the differential equation $3 - (\frac{d^3y}{dx^3})^{7/3} = (\frac{dy}{dx})^5$ are respectively

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