Solving equations and differential equations—MATLAB

Analytical solution:

 

• Solving equations:

[x1,x2,x3,...]=solve（‘eq1’,'eq2','eq3',......,'x1','x2','x3','....'） 

S=solve（‘eq1’,'eq2','eq3',......,'x1','x2','x3','....'）

 

1. The first method requires the order of x1, x2, and x3 in the brackets of the solve (consistent with the previous []), and the second has no requirements. eq is an equation, not an expression.
2. It is best to put quotation marks, or not to put quotation marks, but you must use sym, syms and other settings and pre-defined symbols in advance.

 

• Solve the differential equation:

dsolve（‘eq1’,'eq2',....）

Same as above

Numerical Solution

Generally use ode45 (@fun,tspan,y0)

1. Write the sub-functions, use the form of a matrix to represent the differential equations, and the original problem must be converted into n first-order differential equations.

2.y0 is generally a (n*1) vector, and tspan is generally a binary vector

2. You can also use function handles (anonymous functions)

example:

For y'=2t, solve the differential equation

 

tspan = [0,5]; 
y0 = 0; 
[t,y] = ode45(@(t,y) 2*t, tspan, y0);%Method of using function handle