First-order ordinary differential equations are ODEs where the highest derivative in the equation is the first derivative. In general, solving these ODEs are the easiest to do, compared to higher order or partial differential equations.
Observe that we have several tools to solve these ODEs: separation of variables, integrating factor, and the method of undetermined coefficients all hold and should give us a similar answer for non-homogeneous equations.
Tools and concepts
- Separation of variables
- Integrating factor
- Method of undetermined coefficients (for non-homogeneous ODEs)
- Direction field
- Phase plot