The order and degree of the differential equa | vedclass

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(A) Given differential equation is $\frac{d^{2} y}{d x^{2}} = \sqrt[3]{1-\left(\frac{d y}{d x}\right)^{4}}$.To find the order and degree,we first elim

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$2, 3$

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(A) Given differential equation is $\frac{d^{2} y}{d x^{2}} = \sqrt[3]{1-\left(\frac{d y}{d x}\right)^{4}}$.To find the order and degree,we first eliminate the radical sign by cubing both sides:$\left(\frac{d^{2} y}{d x^{2}}\right)^{3} = 1 - \left(\frac{d y}{d x}\right)^{4}$.The order of a differential equation is the order of the highest derivative present. Here,the highest derivative is $\frac{d^{2} y}{d x^{2}}$,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 $\frac{d^{2} y}{d x^{2}}$ is $3$.Therefore,the order is $2$ and the degree is $3$.

The order and degree of the differential equation $\frac{d^{2} y}{d x^{2}}=\sqrt[3]{1-\left(\frac{d y}{d x}\right)^{4}}$ are respectively

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