The order and degree of the differential equation $\left(1+\frac{\mathrm{d} y}{\mathrm{~d}…
The order and degree of the differential equation
$\left(1+\frac{\mathrm{d} y}{\mathrm{~d} x}\right)^{\frac{1}{3}}=\sqrt{\frac{\mathrm{d}^2 y}{\mathrm{~d} x^2}}$ are respectively.
3,1
3,2
2,3
2,1
Solution
$\left(1+\frac{\mathrm{d} y}{\mathrm{~d} x}\right)^{\frac{1}{3}}=\sqrt{\frac{\mathrm{d}^2 y}{\mathrm{~d} x^2}} \Rightarrow\left(1+\frac{\mathrm{d} y}{\mathrm{~d} x}\right)^2=\left(\frac{\mathrm{d}^2 y}{\mathrm{~d} x^2}\right)^3$
order $=2$ and degree $=3$.