dx2/dt^2+5dx/dt+6x=f(t)

f(t)=4e(-t)u(t)

x(0)=1

x'(0)=2

so I change it to first order

dx/dt=z

dz/dt=-5z-6x+f(t)

ti=0 ;tf=5s

h or deltat=0.1 sec increment

plot x(t)

program:

A=[0 1;-6 -5];

B=[0;1];

f=inline('4*exp(-t)');

t=0;

t1=5;

x=[0;1];

h=0.1;

n=(t1-t)/h;

for i=1:n

k1=A*x+B*f(t);

k2=A*(x+h*k1/2)+B*f(t+1/2*h);

k3=A*(x+h*k2/2)+B*f(t+1/2*h);

k4=A*(x+h*k3)+B*f(t+h);

k=(k1+2*k2+2*k3+k4)/6;

t=t+h;

x=x+h*k;

end

h

x

k1

k2

k3

k4

k

t

x

plot(t,x)

this is what I have but I'm not sure if I'm doing this right and