need help with #3

L. (3Upts) Consider the following ivp I)(24), 2(0) = 1.5. ut show that this ivp has a unique solution that exists everywhere on (-00, oo). Sk etch the graph of this solution with explanations (monotonicity, concavity,..) ow that the following initial value problem has a unique solution that exists for all t. cos(a) cos(et), a” +sin(a”) cos(a’) i r(0)-1, r”(0) = 0 . 4. (30 pts) Consider the following ivp r, y, 2x + y + sin t, 2x + 3y + t, with the initial conditions x(0)–1 and y(0) = 2. i) (5pts) Rewrite the ivp in the vector form X’ – AX +f and X(0) – Xo. Specify A, f. ii) (15pts) Compute eta, iii) (10pts) Write down the formula for the solution to the ivp.