Differential equations are equations where the unknowns are functions.

The equations contain various derivatives and exponentials of these functions.

If the differential equation contains a function of one variable, then it is called an ordinary differential equation (ODE); if it contains a function of two or more variables, then it is called a partial differential equation.

Here is the cast list:

The variable of the function

The function

shortly

And here is an equation

Order

It indicates the highest derivative of the function in the equation.

Linearity

If the equation includes the unknown function and its derivatives only in first-degree form, then the equation is linear.

Here, for instance, the order is 2.

This equation is not linear.

Now let’s get to the funniest matter: finding the solution.

We will group the differential equations based on their types, and then discuss the solution methods for each group.

But there is a snag.

Namely, some badass physicists don’t use x for the variable, instead, they use t, and then the function is not called y, but x.

The reason is that differential equations are often used to describe processes where the variable is time, commonly denoted by t.

If we denote the variable by t and the function by x, then the equation will be:

In this case the symbol for differentiation is a dot.

And now, let’s see how to solve these equations.