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  4. The order degree of the differential equation [1+((d y/d x))5](1/3)=(d2 y/d x2) are respectively

Q. The order $\&$ degree of the differential equation $\left[1+\left(\frac{d y}{d x}\right)^{5}\right]^{\frac{1}{3}}=\frac{d^{2} y}{d x^{2}}$ are respectively

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Solution:

$\left[1+\left(\frac{d y}{d x}\right)^{5}\right]^{\frac{1}{3}}=\frac{d^{2} y}{d x^{2}}$ cubing on both sides $1+\left(\frac{d y}{d x}\right)^{5}=\left(\frac{d^{2} y}{d x^{2}}\right)^{3}$
$\therefore$ order is $2$ and degree is $3$.

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