Please help me

4. (12 points) Let's consider what is called a boundary value problem, or BVP. This is when, instead of solving a second order ODE with two initial conditions, we solve the ODE with two boundary conditions. For example, you may want the conditions a:(0) = 1 and air/3) = 1 to hold for your solution. Here i = 0 and t = 7r/ 3 are thought of as the boundaries. This is related to control. problems, where one requires a particular behavior to happen and tweaks their design to make it happen. (a) Solve the BVP given by the ODE r\" + Qr' = 0 and the boundary conditions mm) = 1 and 33(1r/3) = 1. How many solutions to this BVP did you nd? (b) If you wanted to obtain the exact same solution a:(t) you got in (a) from solving 3:\" + 9.7:" = 0, but using initial conditions instead of boundary values, what initial conditions would you usel'? (c) Solve the BVP given by the ODE 3:\" + 993 = 0 and the boundary conditions 3(0) = 1 and 33(17/3) = 1. How many solutions to this BVP did you nd