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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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The correct answer is:
2,3
Given differential equation is
$$
\begin{aligned}
& \frac{d^{2} y}{d x^{2}} &=\sqrt[3]{1-\left(\frac{d y}{d x}\right)^{4}} \\
\Rightarrow &\left(\frac{d^{2} y}{d x^{2}}\right)^{3} &=1-\left(\frac{d y}{d x}\right)^{4} \\
\therefore & \quad \text { Order } &=2, \text { degree }=3
\end{aligned}
$$
$$
\begin{aligned}
& \frac{d^{2} y}{d x^{2}} &=\sqrt[3]{1-\left(\frac{d y}{d x}\right)^{4}} \\
\Rightarrow &\left(\frac{d^{2} y}{d x^{2}}\right)^{3} &=1-\left(\frac{d y}{d x}\right)^{4} \\
\therefore & \quad \text { Order } &=2, \text { degree }=3
\end{aligned}
$$
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