System of Linear First-Order DE Homog Linear System System of Linear First-Order DE (constant Coeff) Distinct real Eigenvalues repeated real Eigenvalues Non-real Eigenvalues System of Linear First-Order DE (Non-homog) Variation of Parameters

Homogeneous nXn Linear System Remarks: nXn Homog System We need to find n-lin. Indep sols: General solution is

System of Linear First-Order DE Homog Linear System System of Linear First-Order DE (constant Coeff) Distinct real Eigenvalues repeated real Eigenvalues Non-real Eigenvalues

Distinct real Eigenvalues Theorem : nXn Homog System Lin. Indep sol General solution is Solve:

Distinct real Eigenvalues Theorem : nXn Homog System Lin. Indep sol General solution is Solve:

Complex Eigenvalues () Theorem : 2-Lin. Indep sol Solve:

Repeated real Eigenvalues () Solve:

Repeated real Eigenvalues ()

Repeated real Eigenvalues () Solve:

Repeated real Eigenvalues () Solve:

Homog Linear System 2X2 system 2 complex 2 real distinct 2 real repeated