1. (20 pts) Solve the IVP:

y'''' - 4y''' + 4y'' = 0, y(0) = 0, y'(0) = 0, y''(0) = 0, y'''(0) = 0.

Solution

The given equation is homogeneous. It's obviously satisfied by y(t) = 0 identically. This function also satisfies the initial conditions and, therefore, solves the IVP.

Answer

y(t) = 0.