The former is mainly solved by characteristic equation, which is also relatively simple. Just recite three formulas. The latter is the general solution of the nonhomogeneous equation plus the special solution of the corresponding homogeneous equation, which means that the special solution of the nonhomogeneous equation is difficult to find. The general solutions of homogeneous and nonhomogeneous differential equations contain all solutions.
Mathematical description of differential equation;
Many basic laws of physics or chemistry can be written in the form of differential equations. In biology and economics, differential equations are used as mathematical models of complex systems. The mathematical theory of differential equations first appeared together with the corresponding field of equation science, and the solutions of differential equations can be used in this field. However, sometimes two completely different scientific fields will form the same differential equation. At this time, the mathematical theory corresponding to differential equations can show the consistent principle behind different phenomena.
Solution thinking
To do this sub-question, we must first distinguish which of the three types each question is, and then we can start to do it. See if there is a y in the equation. If there is Y, it must be the third category. If not, it is the first or second category. Next, let's see if y has a first derivative. If so, it is the second category. If not, it is the first category.
If and only if there is neither y nor x, it can be the third category or the second category. Which one is specific depends entirely on which one works. The difference between the second category and the third category is that the second derivative of y is different.