Classify each given differential equation as to type and order. Classify the ordinary differential equation as to linearity and identify initial-value problem or boundary value problem Indicate what method(s) of solution can be applied for each ODE. Solve 4 Solution Third order linear constant coefficient homogeneous ODE. Solve by solving auxiliary equation r^3 +10r^2 +25r=0 r(r+5)^2=0 r=0, -5 multiplicity 2 So a general solution is A +Be^(-5t) +Cte^(-5t)= Y(t).

1. Classify each given differential equation as to type and order. Classify the ordinary differential
equation as to linearity and identify initial-value problem or boundary value problem Indicate
what method(s) of solution can be applied for each ODE. Solve 4
Solution
Third order linear constant coefficient homogeneous ODE. Solve by solving
auxiliary equation r^3 +10r^2 +25r=0 r(r+5)^2=0 r=0, -5 multiplicity 2 So a general solution is
A +Be^(-5t) +Cte^(-5t)= Y(t)