The first axis: differential equations:

Let y be a function of the variable x that can be differentiated n times. We call each differential equation of order n

An equation of the form:

Where: y is the nth derivative of y

The general form of y(x) that satisfies equation (1) is called the general solution of the differential equation. We call a special solution to the differential equation. Every solution satisfies some special conditions, and these conditions are called the initial conditions.

Order and degree of the differential equation:

The order of the differential equation: It is the order of the highest differential coefficient in the equation

Degree of the differential equation: It is the degree (strength) of the highest differential coefficient in the equation, provided that all differential coefficients are free of fractional powers.

Example:

• y’’’2+2y’3-5y=0 is a third-order and second-order differential equation.

• y’+xy=x2 is a differential equation of first order and first order.

• y’’’+y’3+y=cos x is a third-order and first-order differential equation.

Types of differential equations:

Differential equations can be divided into two parts, ordinary differential equations and partial differential equations.