October 7

4.3.  Fundamental Solutions of Homogeneous Equations

objective

• to be able to determine whether functions are linearly dependent or linearly independent
• to be able to find general solutions when given solutions
• to be able to find particular solutions when given solutions and initial conditions

• general solution
• representation of solutions (homogeneous case)
• Wronskian, W[y₁,y₂](x)
• Fundamental solution set
• linearly independent
• linearly dependent
• linear dependence of functions

solved problems - using key ideas

• determining linear dependency of functions using the definition, #2,5
• finding a general solution, #8
• examining solution sets of a given differential equation, #13
• studying Wronskians, #15a,b
• linear dependence of three functions, #24,25a
• Wronskian of three functions, #27a

SOLUTION.