The order and degree of the differential equa | vedclass

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

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$2, 3$

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(A) Given the differential equation: $\sqrt{\frac{d^2 y}{d x^2}}=\sqrt[3]{\left(\frac{d y}{d x}\right)^4+2}$.To find the order and degree,we first remove the radicals by raising both sides to the power of $6$ (the least common multiple of $2$ and $3$):$\left(\left(\frac{d^2 y}{d x^2}\right)^{1/2}\right)^6 = \left(\left(\left(\frac{d y}{d x}\right)^4+2\right)^{1/3}\right)^6$.This simplifies to: $\left(\frac{d^2 y}{d x^2}\right)^3 = \left(\left(\frac{d y}{d x}\right)^4+2\right)^2$.The highest order derivative present is $\frac{d^2 y}{d x^2}$,so the order is $2$.The power of the highest order derivative after rationalizing is $3$,so the degree is $3$.Therefore,the order is $2$ and the degree is $3$.

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

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