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
`(\mathrm d^2y)/(\mathrm dx^2)`).

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


`F\left((\mathrm d^2y)/(\mathrm dx^2),(\mathrm dy)/(\mathrm dx),y,x\right)=0\iff f_2(x)(\mathrm d^2y)/(\mathrm dx^2)+f_1(x)(\mathrm dy)/(\mathrm dx)+f_0(x)y+g(x)=0`

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