Midterm 2 Material - Linear
Linear Equations of Order 2 and Higher
Distinct Real Roots
Constant Coefficients with Distinct Real Roots
Complex Conjugate Roots
Constant Coefficients with Complex Conjugate Roots
Repeated Roots
Constant Coefficients with Repeated Roots
Reduction of Order
Recovering the full solution set given one homogeneous solution
Cauchy-Euler Equations
The Monomial Analogue of the Constant Coefficients Equations
Exponential Functions
Finding the right constant multiple
Polynomial Functions
Using either Iterative Refinement or Undetermined Coefficients
Sine and Cosine Functions
Using either Iterative Refinement or Undetermined Coefficients
Exponential Functions with Conflicting Roots
The desired exonential is alredy a homogeneous solution
Variation of Parameters
A Determinant and Integration Heavy Method for finding Particular Solutions
Extra Variation of Parameters Problems (external reference)
Warning: These problems can be very tedious. Practice these sparingly if at all.