Section 3.1, Problems 2, 4,,with the following addition: Find the solution of the given initial-value problem assuming that the solutions u, v, z of the same system with the initial conditions (1,0,0)T , (1,1,0)T, (1,1,1)T, respectively, are known.

In each of Exercises 1-3 convert the given differential equation for the sin- gle variable y into a system of first-order equations. 1. day , dry + 2. d' y + cosy = e' 3. + =1 di dt 3 di4 di2 4. Convert the pair of second-order equations dzy + 3. dz + 2y= 0, d 2z + 3 dy dt2 dt dt +2z=0 into a system of 4 first-order equations for the variables X1 =y, X2 = y's X3=z, and x4= z'