The order and degree of the differential equa | vedclass

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(B) Step $1$: Write the given differential equation: $(\frac{d^3y}{dx^3})^{\frac{2}{3}} = 3\frac{d^2y}{dx^2} - 5\frac{dy}{dx} - 4$.Step $2$: To find t

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$3, 2$

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(B) Step $1$: Write the given differential equation: $(\frac{d^3y}{dx^3})^{\frac{2}{3}} = 3\frac{d^2y}{dx^2} - 5\frac{dy}{dx} - 4$.Step $2$: To find the degree, the equation must be a polynomial in terms of derivatives. Remove the fractional exponent by raising both sides to the power of $3$: $((\frac{d^3y}{dx^3})^{\frac{2}{3}})^3 = (3\frac{d^2y}{dx^2} - 5\frac{dy}{dx} - 4)^3$.Step $3$: This simplifies to $(\frac{d^3y}{dx^3})^2 = (3\frac{d^2y}{dx^2} - 5\frac{dy}{dx} - 4)^3$.Step $4$: The order is the highest derivative present, which is $3$. The degree is the power of the highest derivative after rationalizing, which is $2$. Thus, the order is $3$ and the degree is $2$.

The order and degree of the differential equation $(\frac{d^3y}{dx^3})^{\frac{2}{3}} - 3\frac{d^2y}{dx^2} + 5\frac{dy}{dx} + 4 = 0$ are respectively:

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