In problems a-f, a differential equation is given along with the field or problem area in which it arises. Classify each as an ordinary differential equation (ODE), or 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. a. dy -+2y=0 (Hermite's equation, quantum-mechanical harmonic dx oscillator) b. du du =0 (Laplace's equation, potential theory, electricity, heat, aerodynamics) dx C. -=k(4-x)(1-x), where k is a constant. (chemical reaction rates) dt d. Al-vay+ 2x=0 (Kidder's equation, flow of gases through a porous medium) dx e. gav d.x4 =x(1-x) (deflection of beams) ON 1 ON f. ON -+ KN, where k is a constant. (nuclear fission) at r or