Problem 3 (25 points) For each case defined below, write a s…

Problem 3 (25 points) For each case defined below, write a sample ordinary differential equation (ode), along with any required additional conditions. Include the identification of the independent and dependent variables. An initial value problem defined by a second order linear homogeneous ode with constant coefficients having a non-trivial solution. A boundary value problem involving a fourth order linear nonhomogeneous ode. A first order homogeneous nonlinear ode.