General solution and special solution in differential equation What is the difference between them? What is the difference between them and the general solution and special solution of linear equations?

General solution and special solution in differential equation What is the difference between them? What is the difference between them and the general solution and special solution of linear equations?

First of all, there is something wrong with your classification, because differential equation and linear equation are just two completely different classifications, which can be differential linear, differential nonlinear, linear and nonlinear. It's better for you to take a textbook with you
When you ask this question, you should know what a linear equation looks like?
x^n+a1x^(n-1)+a2x^(n-2)+… +a(n-1)x+an=0
This is a linear equation. If the right end is equal to 0, it means that it is a homogeneous equation; if the right end is not equal to 0, it means that it is a non-homogeneous equation
This is for homogeneous and non-homogeneous equations
Then, the differential equation is similar, except that the k-th power of the left end X becomes the k-th derivative of X with respect to t
That is x ^ (n) + A1 * x ^ (n-1) + +A (n-1) * x '+ an * x = 0 (x ^ (k) is the k-th derivative of x)
Similarly, the right end is equal to 0, which is a homogeneous differential equation, the solution is the general solution x (T); if the right end is not equal to 0, but a f (T), then the solution is a special solution x * (T)!
The solution of the whole differential equation x = x (T) + X * (T)!