Second order linear diff equations:

  Complex Roots:  (\( y = y(t)\))  Formula derivation and some examples

1. Find the fundamental set of solutions and general solution of the diff equations.  solution

a. \( y''+y=0 \)    

b. \( y''- 4y'+5y=0 \)

2. Find the solution of the given initial value problem.

a. \(y''+4y=0; \quad y(0)=0, \:  y'(0)=1\)  solution

b. \(16y''-8y'+145y=0; \quad  y(0)=-2, \:  y'(0)=1\)  solution

c. \(y''-2y'+5y=0, \: \:y(\pi/2)=0, \: y'(\pi/2)=2 \)   solution I     solution II