The order and degree of the differential equa | vedclass

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(D) To find the order and degree,we first eliminate the fractional exponent by raising both sides of the equation to the power of $4$.$\left( \frac{d^

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$2$ and $4$

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(D) To find the order and degree,we first eliminate the fractional exponent by raising both sides of the equation to the power of $4$.$\left( \frac{d^2y}{dx^2} \right)^4 = y + \left( \frac{dy}{dx} \right)^2$The order of a differential equation is the order of the highest derivative present. Here,the highest derivative is $\frac{d^2y}{dx^2}$,so the order is $2$.The degree of a differential equation is the power of the highest derivative when the equation is expressed as a polynomial in derivatives. Here,the power of $\frac{d^2y}{dx^2}$ is $4$.Thus,the order is $2$ and the degree is $4$.

The order and degree of the differential equation $\frac{d^2y}{dx^2} = \left\{ y + \left( \frac{dy}{dx} \right)^2 \right\}^{1/4}$ are:

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