2nd order homogenous DE

integrating factor

2nd order DE

Uniqueness + existeness theorm 2nd order DE

Linear combination + superposition principle theorm

general solution

linear independence !!!!!!

Solving 2nd order homogenous ODE with constant coefficients

ansantz: y = e^rt

Solvign 2nd order homogenous ODE with non constant coefficients

ansantz: y = t^r

reduction of order (repeated roots)

• you need to do this manually with non-constant equations

• However for constant equations a shortcut is:
  x = C1 + (t)C2