Water, but we still need to briefly introduce ordinary differential equations. Sometimes people find mathematics difficult to understand, because many textbooks write a lot of difficult words in pursuit of absolute rigor, so we need some people who can understand them to translate these obscure words into easy-to-understand people. This is the ordinary differential equation.

When we were in junior high school, we learned to solve equations. The final solution is often a number, while the ordinary differential equation is a (function). The ordinary differential equation is often an equation with differential (derivative) or several higher-order differentials (derivatives). This complex coupled differential equation is used to restore the original equation of function, which is the meaning of ordinary differential equation.

Why is there such an equation? Or why do you think this seemingly weird problem is difficult to solve (ordinary differential equations are difficult for beginners to understand), because in daily life, it is difficult for us to observe the corresponding problems in detail, such as the distribution of gas density or heat in the atmosphere, which is often difficult for us to measure directly. At this time, we often introduce other variables to solve the problem, such as measuring the speed and trajectory of its movement with several hot air balloons. Time and other variables, at this time we can indirectly get some data of the atmosphere through these variables (a mathematical idea-one-to-one correspondence rule). Some data we get are often differential equations or partial differential equations that we want to solve. At this time, it is necessary to solve ordinary differential equations to restore the original equations.

The solutions of first-order differential equations can be divided into the following categories.

(1) variables can be separated.

(2) Variable and separable.

(3) First order linear differential equation

(4) Bernoulli equation