Second order linear diff equations:

A. Real and Distinct Roots:    Formula Derivation and some examples

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

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

c. \( y''+3y'-4y=0 \)     d. \( y''-7y'+4y=0 \)

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

a. \( y''+y'-2y=0, \quad  y(0)=2, \: y'(0)=1\)   solution

b. \( y''+3y'=0, \quad y(0)=-2, \: y'(0)=3\)   solution

c. \( y''+8y'-9y=0, \quad y(1)=1, \: y'(1)=0\)   solution