The order and degree of the differential equa | vedclass

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(D) Given the differential equation: $\left(\frac{d^2 y}{d x^2}\right)^{1/3} = \left(\frac{d^3 y}{d x^3}\right)^{1/2}$.To eliminate the fractional exp

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$3, 3$

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(D) Given the differential equation: $\left(\frac{d^2 y}{d x^2}\right)^{1/3} = \left(\frac{d^3 y}{d x^3}\right)^{1/2}$.To eliminate the fractional exponents,raise both sides to the power of $6$ (the least common multiple of $2$ and $3$):$\left(\left(\frac{d^2 y}{d x^2}\right)^{1/3}\right)^6 = \left(\left(\frac{d^3 y}{d x^3}\right)^{1/2}\right)^6$.This simplifies to: $\left(\frac{d^2 y}{d x^2}\right)^2 = \left(\frac{d^3 y}{d x^3}\right)^3$.The highest order derivative present is $\frac{d^3 y}{d x^3}$,so the order is $3$.The power to which the highest order derivative is raised is $3$,so the degree is $3$.Therefore,the order and degree are $3$ and $3$ respectively.

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

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