1. 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

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

3. 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

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

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

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

7. Repeated real Eigenvalues ()
Solve:

8. Repeated real Eigenvalues ()

9. Repeated real Eigenvalues ()
Solve:

10. Repeated real Eigenvalues ()
Solve:

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