The order and degree of the differential equa | vedclass

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(B) Step $1$: The given differential equation is $(\frac{d^3y}{dx^3})^{2/3} - 3 \frac{d^2y}{dx^2} + 5 \frac{dy}{dx} + 4 = 0$.Step $2$: To find the deg

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$3, 2$

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(B) Step $1$: The given differential equation is $(\frac{d^3y}{dx^3})^{2/3} - 3 \frac{d^2y}{dx^2} + 5 \frac{dy}{dx} + 4 = 0$.Step $2$: To find the degree, the equation must be a polynomial in terms of its derivatives. We eliminate the fractional exponent by raising both sides to the power of $3$: $(\frac{d^3y}{dx^3})^2 = (3 \frac{d^2y}{dx^2} - 5 \frac{dy}{dx} - 4)^3$.Step $3$: The highest order derivative present is $\frac{d^3y}{dx^3}$, so the order is $3$.Step $4$: The power to which the highest order derivative is raised after making the equation a polynomial is $2$, so the degree is $2$.

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

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