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EXERCISE 1. In each of Problems 1 through 4, determine the order of the given di e-rential equations; also state whether the equation is linear or nonlinear. +(++=c 2. da: da EXERCISE 2. In each of Problems 1 through 3. verify that each given function is a solu- tion of the differential equation. 1. tys' 5ty +4y = 0, t>0; 2. y" +y = sect, O3. 02 = ut; = 4. In each of Problems (a) and (b), determine (without solving the problem) the largest interval in which the solution of the given initial value problem is certain to exists (and to be unique). (a) (Int)y +y = cot t, y(2)=3 (b) (4 - t²)y' + 2ty = 3/², y(-3) 1 1 EXERCISE 3. In each of Problems 1 through 4, find the general solution of given diffe rential equations. 1. y'+2ty=2te-1 t - dy x 4. da y tey EXERCISE 4. In each of Problems 1 through 5, find the solution of given initial value problem. 1. y'+(2/t)g==(cost)/f, y() =0, t>0 2. ty' +(t+1)y=t, y(In2) = 1. t > 0 3. y =r(z²+1)/4y³, y(0) = -1/v2 4. 1 5. xdx + ye "dy =0, y(0) 1 EXERCISE 5. A glucose solution is administered intravenously into the boodstream at a constant rate r. As the glucose is added, it is converted into other substances and removed from the bloodstream at a rate that is proportional to the concentration at the time. Thus a model for the concentration C = C(t) of the glucose solution in the bloodstream is dC =r-kC dt where k: is a positive constant. 1. Suppose that the concentration at time t = 0 is Co. Determine the concentration at any time t by solving the differential equation. 2. Assuming that Co 2

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