Question

d^2y/dx^2=sqrt(1+(dy/dx)^2 state the order of the given ordinary differential equation. Determine whether the equation is linear or nonlinear.

Answer 1

This is a second-order ODE since the highest order derivative is 2 (from $\dfrac{\mathrm d^2y}{\mathrm dx^2}$).

It's not linear because it doesn't take the form

$F\left(\dfrac{\mathrm d^2y}{\mathrm dx^2},\dfrac{\mathrm dy}{\mathrm dx},y,x\right)=0\iff f_2(x)\dfrac{\mathrm d^2y}{\mathrm dx^2}+f_1(x)\dfrac{\mathrm dy}{\mathrm dx}+f_0(x)y+g(x)=0$

and it's not possible to rewrite it as such.