## Differential equations (DEQ): Important basics + 4 solving methods

Here you will learn the basics of differential equations (DGL), what types there are (ordinary, partial, linear, homogeneous) and 4 solving methods (separation of variables, variation of constants, exponential and separation ansatz).

## Content of the lesson

- What is a differential equation? Here you will learn how to identify a differential equation and which problems involve DEQ's.
- Different notations of a differential equation Here you will learn the Leibniz, Newton and Lagrange notations of a differential equation.
- What should I do with a differential equation? Here you will learn what it means to solve a DEQ and whether it is always possible.
- How to identify a differential equation What characterizes a DEQ and how do I know if I have a DEQ in front of me? This is the first question you have to answer before solving a DEQ!
- Classification: Which DEQ types are there? Here you will learn how to recognize when a DEQ is ordinary, partial, linear, homogeneous, inhomogeneous, and of what order it is.
- Constraints: Boundary and initial conditions Here you will learn why constraints to a DEQ are important and what the difference is between boundary and initial conditions.
- Solving method #1: Separation of variables Here you will learn a method to solve ordinary homogeneous linear DEQ of 1st order. Or you can directly use the derived formula.
- Solving method #2: Variation of constants Here you will learn a method to solve ordinary inhomogeneous linear DEQ of 1st order.
- Solving method #3: Exponential ansatz Here you will learn a method to solve linear DGL of any order.
- Solving method #4: Product ansatz (separation ansatz) With this ansatz you can convert partial differential equations into ordinary differential equations and then solve them with other methods.