Exercise 1 Most differential equations cannot be solved analytically (yielding a closed-form solution in terms of elementary functions) and instead must be solved numerically on a grid. For the dif- ferential equations which we can solve analytically, the particular method for obtaining a solution depends on identifying key properties of the equation: order, degree, linear vs. nonlinear, separa- ble vs. non-separable, homogeneous vs. inhomogeneous, and of course, whether it is an ordinary or partial differential equation. Identify the specied property of the set of differential equations each in subexercise. (a) Identify by equation number which differential equation has the highest order: d_3y+ dx3+ xdy-I-=x2y 0 _fa a_f_0 ax+ 6y 1/\" + 2y" +y = cos(x) (b) Identify by equation number which differential equation(s) is/are separabie: Exercise 2 Considering halogenation reaction, H2 + X2 > 2HX where X2 is some diatomic halogen. Its rate law is: = k [H2] per/2 (10) Let a he the initial concentration of diatomic hydrogen and b be the initial concentration of diatomic halogen and x be the concentration hydrogen halide. (a) Write Eq.10 in terms of x,a,b. (b) Using the equation you transcribed in (a), nd x(t) for the case where initial concentrations are equal a = b. Use the initial condition that the initial concentration of product is zero, x(0) = 0. Exercise 3 An IV supplies a dilute solution of glucose, CH1206 into a patient's bloodstream at a constant rate r. As the glucose is added, it is metabolized into and removed from the bloodstream at a rate, k, proportional to the instantaneous concentration of glucose, [C6H1206](t). The equation describing this process is: d [C6H1206] = r - k[C6H1206] (11) dt (a) Relabel the concentration [C6H1206](t) with the variable C and suppose that the concentration at time t = 0 is Co. Determine the concentration at any time C(t) by solving the differential equation (Eq. 11). (b) Provided that Co