Basic definitions

Definition 2.1. Adifferential equation is an equation which contains an argument, a function and one or more derivatives of the differentiable function, that is

Definition 2.2. The order of a differential equation is the highest order a derivative.

Differential equations can be linear and nonlinear. For example,

Fist order, linear: ; .

Third order, nonlinear: .

Definition 2.3. We call a function a solution of a differential equation if and its derivatives satisfy the equation.

The process of finding of the solution is called integration of a differential equation.

Definition 2.4. A function which gives all solutions of a differential equation is called the general solution of the equation.

Definition 2.5. The general solution which was found in implicit form is called the general integral of the equation.

To solve a differential equation means to find its general integral.

Definition 2.6. The particular solution is a solution which is obtained from the general solution by replacing arbitrary constants by some admissible numerical values.

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