Laplace with Heaviside step function solving with ode45

I dont understand why I keep getting an error, can you please explain to me why and how I can fix this?

syms s t Y
f = heaviside(t-1)- heaviside(t-2);
X = laplace(f);
Sol = X ./(s^2+3*s+2);
sol = symfun(ilaplace(Sol),t);
pretty(sol)

                 / exp(2 - 2 t)                1 \                    / exp(4 - 2 t)                1 \
heaviside(t - 1) | ------------ - exp(1 - t) + - | - heaviside(t - 2) | ------------ - exp(2 - t) + - |
                 \       2                     2 /                    \       2                     2 /

tspan = [0 5];
ic = [0 0];

fn = @(t,Y) [Y(2); (heaviside(t-1)- heaviside(t-2) - 3*Y(2) - 2* Y(1))];   
[t,Y] = ode45(fn,tspan,ic);

Index exceeds the number of array elements. Index must not exceed 1.

Error in indexing (line 968)
R_tilde = builtin('subsref',L_tilde,Idx);

Error in solution>@(t,y)[Y(2);(u-Y(3)-3*Y(2)-2*Y(1))] (line 12)
fn = @(t,y) [Y(2); (u - Y(3) - 3*Y(2) - 2* Y(1))];

Error in odearguments (line 92)
f0 = ode(t0,y0,args{:}); % ODE15I sets args{1} to yp0.

Error in ode45 (line 104)
odearguments(odeIsFuncHandle,odeTreatAsMFile, solver_name, ode, tspan, y0, options, varargin);

hold on
plot(t,y(:,1))
fplot(sol, [0 5])
grid on 
xlabel('x')
ylabel('y')
legend('Ode45' ,'Solved' )
hold off 

Answer 1

[Torsten]

You try to access Y(3), but you have only two differential equations for Y(1) and Y(2), I guess.

And the "Y" must be "y" because your list of inputs is t and y, not t and Y.

And ode45 is a numerical solver - it does not accept symbolic inputs like your "u".

[Tashanda Rayne]

Thank you, now when I try to graph it, it will not graph them together. How can I accomplish that?

syms s t Y

f = heaviside(t-1)- heaviside(t-2);

X = laplace(f);

N = 1000;

x = linspace( 0, 70,N);

for i = 1:1:N

Sol = X ./(s^2+3*s+2);

sol = @(t) symfun(ilaplace(Sol),t);

end

u = heaviside(x-1)- heaviside(x-2);

k = @(x,Y) [Y(2); (heaviside(x-1)- heaviside(x-2) - 3*Y(2) - 2* Y(1))];

[x,Y] = ode45(k, [0 5], [0 0]);

hold on

plot(x,Y(:,1))

fplot(sol, [0 5])

grid on

xlabel('x')

ylabel('y')

legend('Ode45' ,'Solved' )

hold off

[Torsten]

fplot(sol(t), [0 5])

instead of

fplot(sol, [0 5])

[Tashanda Rayne]

Thank you