How to solve 1st Order System of Differential Equations in MATLAB?

Question:

How to solve 1st Order System of Differential Equations in MATLAB?

Answer:

System of Differential equations can be solved symbolically in MATLAB by using built-in command "dsolve"

clear all; clc; close all
syms x(t) y(t) z(t)
dx = diff(x,t);
dy = diff(y,t);
dz = diff(z,t);
eqn1 = dx == 2*x + y + z;
eqn2 = dy == x + 2*y + z;
eqn3 = dz == -2*x + -2*y + z;
sol = dsolve([eqn1 eqn2 eqn3],t);
x = sol.x
y = sol.y
z = sol.z

OUTPUT

x =
 
C3*((exp(2*t)*sin(3^(1/2)*t))/4 + (3^(1/2)*exp(2*t)*cos(3^(1/2)*t))/4) 
- C2*((exp(2*t)*cos(3^(1/2)*t))/4 - (3^(1/2)*exp(2*t)*sin(3^(1/2)*t))/4) - C1*exp(t)
 
 
y =
 
C1*exp(t) - C2*((exp(2*t)*cos(3^(1/2)*t))/4 - (3^(1/2)*exp(2*t)*sin(3^(1/2)*t))/4) 
+ C3*((exp(2*t)*sin(3^(1/2)*t))/4 + (3^(1/2)*exp(2*t)*cos(3^(1/2)*t))/4)
 
 
z =
 
C2*exp(2*t)*cos(3^(1/2)*t) - C3*exp(2*t)*sin(3^(1/2)*t)