Second order linear diff equations:

 Equal Roots:  (\( y = y(t)\))  Formula Derivation and some examples

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

a. \( y''-6y'+9y=0 \)    

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

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

a. \(9y''-12y'+4y=0; \quad  y(0)=2, \:  y'(0)=-1\)    solution

b. \(y''+4y'+4y=0; \quad  y(-1)=2, \:  y'(-1)=1\)   solution