Only for the additional question. 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. (Note: (1,0,0)T means the column vector with entries 1,0,0).

In each of Exercises 1-3 convert the given differential equation for the sin- gle variable y into a system of first-order equations. + * * ) -0 2 day + cosy = e' d4 day + =1 di4 4. Convert the pair of second-order equations d'z 13 dy dt2 + 31 dz + 2y = 0, dt2 di + 2z= 0 into a system of 4 first-order equations for the variables X2=y', x3=z, and x4= z'