A differential equation is given along with the field or problem area in which it arises. Classify it as an ordinary differential equation (ODE) or a partial differential equation (PDE), give the order, and indicate the independent and dependent variables. If the equation is an ordinary differential equation, indicate whether the equation is linear or nonlinear.
y[1 + (dy/dx)^2] = C, where C is a constant
(brachistochrone problem, calculus of variations)
Classify the given differential equation. Choose the correct answer below.
partial differential equation
linear ordinary differential equation
nonlinear ordinary differential equation
The order of the differential equation is .
(Type a whole number.)
The independent and the dependent