I should get a straight line graph in this equation after substituting initial conditions. I dont know where I am getting wrong. Can anyone help me with this?

tspan=[0,1];
z0=[0,0.01,0,0]; %initial position and velocity
%[x0,vx0,y0,vy0]
%solve the ODEs
[t, z]=ode45(@rhs,tspan,z0);
% Unpack the variables
x1=z(:,1);
v1=z(:,2);
x2=z(:,3);
v2=z(:,4);
%Plot the results
plot(t,v1);
title(' x1 vs t');
xlabel('t(s)');
ylabel('x1(m/s)');

figure
plot(t,v2);
title(' x2 vs t');
xlabel('t(s)');
ylabel('x2(m/s)');

%set grid,xmin,xmax,ymin,ymax
%___________________
function zdot=rhs(t, z)
x1=z(1); v1=z(2); x2=z(3); v2=z(4);
%put in values for mass ,C and g below
m=1;
k=1;
c=0.001;
h=0.01;
% the linear momentum balance equation
x1dot=v1;
v1dot=0;
x2dot=v2;
v2dot=(k/m)*(x1-x2)-(c/h*m)*v2;
zdot=[x1dot;v1dot;x2dot;v2dot];
end

Answer 1

[Torsten]

For which solution variable do you expect a line as solution ?

syms t y(t)
Dy = diff(y,t);
D2y = diff(y,t,2);
m=1;
k=1;
c=0.001;
h=0.01;
eqn = D2y==(k/m)*(0.01*t-y)-c/(h*m)*Dy;
conds = [y(0)==0,Dy(0)==0];
ysol = dsolve(eqn,conds)

ysol = 

fplot(ysol,[0 1])
grid on