MATLAB: Ordinary Differential Equations using laplace transform and plotting

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For the given ODE, i have used laplace transform to derive my ans. However I need to plot t towrads infinity but i am unsure as to how to code in MATLAB. May I know how to troubleshoot this?
This is the MATLAB code used to solve the ODE:
syms s t Y;
f = exp(t);
F = laplace(f,t,s);
Y1 = (s*Y);
Y2 = (((s^2)*Y)-1);
Sol = solve((9*Y1)+(3*Y2)+(3*Y)-F, Y);
sol = ilaplace(Sol,s,t);

Best Answer

The solution diverges when t approaches infinity
syms s t Y;
f = exp(t);
F = laplace(f,t,s);
Y1 = (s*Y);
Y2 = (((s^2)*Y)-1);
Sol = solve((9*Y1)+(3*Y2)+(3*Y)-F, Y);
sol = ilaplace(Sol,s,t);
limit:
>> limit(sol, t, inf)
ans =
Inf
plot
fplot(sol, [0 100])
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