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Differential equation, Diff Eq like Wave eq, Order? Homogeneous or…

- - - - Linear
        
        What order?
        
        Initial Value Problem or Boundary Value Problem
        Initial or Boundary Conditions?
        (IVP vs BVP)
        
        IVP
        
        Does it have constant coefficients?
        
        Constant Coefficients
        
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        Non-Constant Coefficients
        
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        BVP
        
        Is it Sturm-Liouville?
        −(py′)′ + qy - λwy = 0
        with Dirichlet, Neumann, or Robin B.C.'s
        
        S-L
        
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        Not S-L
        
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      - Non-Linear
        
        Less common, basically handled with approximations. Worry about those when you get to them on a case by case basis.
  - - - Time Independent
        
        Identify Operator Family
        
        Hemholtz
        ∇² u + k² u =0
        
        What coordinate system?
        
        1D
        
        Homogeneous or Forced?
        
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        2D Cartesian
        
        Did they specify the frequency?
        
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        3D Cartestian
        
        Polar
        
        Spherical
        
        Cylindrical
        
        Poisson
        
        Laplace
      - Time Dependent
        
        Identify Type of T.D. PDE
        
        Wave Equation (hyperbolic)
        
        Are boundary conditions time dependent?
        
        Constant B.C.'s
        
        Separation of variables between time and space
        
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        Time dependent B.C.'s
        
        Heat (parabolic)
        
        Shrodinger (dispersive/unitary)