Editing Differential Equations (section)

== <span style="color: #FFFFFF;">Remembering</span> ==
* '''Differential Equation''' — An equation containing at least one derivative of an unknown function.
* '''Ordinary Differential Equation (ODE)''' — An equation containing derivatives with respect to only one independent variable (e.g., time).
* '''Partial Differential Equation (PDE)''' — An equation containing derivatives with respect to multiple variables (e.g., space and time).
* '''Order''' — The highest derivative present in the equation (e.g., a second-order equation has a $y''$ term).
* '''Linear Differential Equation''' — An equation where the dependent variable and its derivatives appear to the first power and are not multiplied together.
* '''Initial Value Problem (IVP)''' — A differential equation together with a specified value (initial condition) for the unknown function at a given point.
* '''General Solution''' — A solution that includes all possible solutions to a differential equation, usually containing arbitrary constants ($C$).
* '''Particular Solution''' — A specific solution obtained from the general solution by applying initial conditions.
* '''Boundary Conditions''' — Values specified at the boundaries of the domain (common in PDEs).
* '''Homogeneous Equation''' — An equation where every term contains the dependent variable or its derivatives (no standalone constant terms).
* '''Separation of Variables''' — A method for solving ODEs by moving all terms of one variable to one side and the other variable to the other side.
* '''Integrating Factor''' — A function used to multiply a non-separable equation to make it integrable.
* '''Autonomous Equation''' — An equation that does not explicitly depend on the independent variable (usually time).
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