The order and degree of the differential equation $\sqrt{1+\frac{1}{\left(\frac{d y}{d…
The order and degree of the differential equation $\sqrt{1+\frac{1}{\left(\frac{d y}{d x}\right)^{2}}}=\left(\frac{d^{2} y}{d x^{2}}\right)^{\frac{3}{2}}$ are respectively
3,2
2,3
2,2
3,3
Solution
By raising the given equation to the power of 2 , we get
$\begin{aligned}
& 1+\frac{1}{\left(\frac{d y}{d x}\right)^{2}}=\left(\frac{d^{2} y}{d x^{2}}\right)^{3} \\
\therefore &\left(\frac{d y}{d x}\right)^{2}+1=\left(\frac{d^{2} y}{d x^{2}}\right)^{3}\left(\frac{d y}{d x}\right)^{2}
\end{aligned}$
It's order is 2 and degree is 3 .