The order and degree of the differential equa | vedclass

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(C) To find the order and degree of the differential equation,we must first eliminate the fractional exponent.Given equation: $\left[ 4 + \left( \frac

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$2, 3$

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(C) To find the order and degree of the differential equation,we must first eliminate the fractional exponent.Given equation: $\left[ 4 + \left( \frac{dy}{dx} \right)^2 \right]^{2/3} = \frac{d^2y}{dx^2}$Cube both sides to remove the fraction in the exponent:$\left[ 4 + \left( \frac{dy}{dx} \right)^2 \right]^2 = \left( \frac{d^2y}{dx^2} \right)^3$Now,the equation is in the form of a polynomial in terms of derivatives.The highest order derivative present is $\frac{d^2y}{dx^2}$,so the order is $2$.The power of the highest order derivative after making it a polynomial is $3$,so the degree is $3$.Thus,the order is $2$ and the degree is $3$.

The order and degree of the differential equation $\left[ 4 + \left( \frac{dy}{dx} \right)^2 \right]^{2/3} = \frac{d^2y}{dx^2}$ are

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