Homogeneous Ordinary Differential Equation

graph TD; A[Homogeneous Ordinary Differential Equation] --> B((First Order)) A --> C((Second Order)) B --> D{Linear} B --> E{Nonlinear} C --> F{Homogeneous with constant coefficients} C --> G{Homogeneous with variable coefficients} D --> H((Separable Variables)) D --> I((Integrating Factor)) E --> J((Exact)) E --> K((Bernoulli)) F --> L((Characteristic Equation)) F --> M((Auxiliary Equation)) G --> N((Power Series Solutions)) G --> O((Frobenius Method))