# Differential equation solution

1. May 27, 2013

### archanas4743

can any one help me with matlab code for for solving a state homogeneous differential

X=state vector

Xdot(t)=AX(t)+BU(t) U is the control input

i have the values of A and B ,i need the solution for X(t)

2. May 27, 2013

### Simon Bridge

Welcome to PF;
Probably - what have you tried?

3. May 30, 2013

### Mina Samir

you can search the m files on matworks, or use the differential equations simulink

4. May 30, 2013

### Mina Samir

A and B are invertibles so inv(A) and inv(B) exists, do the algebra of matrices to get X(t) in a side, but here d/dtX(t) exist, so you can solve the homogeneous system first by assuming that the control input is the zero vector, the general solution of elements are x_i(t)=Constant_i*exp(lamda_i*t), i=1,2,...N

5. May 30, 2013

### Mina Samir

you solve the characteristic equation which is exactly solvable up to 4th degree after you can refer to numerical methods to find the roots lamdas.