How to solve 2nd ODE equation in numerical and analytical method at same plot graph?

2022 9 28
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更新时间：2022 9 28
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Hello,
I am was looking for help to solve this equation
d^x/dt^2 + dx/dt + x =1
in Matlab, can I get help to solve this equation of plot the numerical solutions and analytical solutions in the same graph and compare them.
with ode45
can anyone help me with this code?

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Star Strider
Star Strider 2022-9-28
Ran in:

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Ran in:
Interesting problem!
I was curious enough to do the entire simulation to see what the results are —
syms x(t) x0 Dx0 T Y
Dx = diff(x);
D2x = diff(Dx);
DEqn = D2x + Dx + x == 1;
xs = dsolve(DEqn, x(0)==x0, Dx(0)==Dx0)
xs = 
xs = subs(xs, {x0,Dx0},{1,1}) % Numerical Initial Conditions
xs = 
[VF,Sbs] = odeToVectorField(DEqn)
VF = 
Sbs = 
DEfcn = matlabFunction(VF, 'Vars',{T,Y})
DEfcn = function_handle with value:
@(T,Y)[Y(2);-Y(1)-Y(2)+1.0]
tspan = [0 10];
[t,x] = ode89(DEfcn, tspan, [1 1]);
figure
fplot(xs, tspan, 'DisplayName','Analytic')
hold on
plot(t, x(:,1), 'DisplayName','Numeric')
hold off
grid
xlabel('Time')
ylabel('x_1(t)')
legend('Location','best')
They match almost exactly.
.

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Shreyas Sangamesh
Shreyas Sangamesh 2022-9-28
Hello,
thank you helping me to solve this problem,
But, we need to use ode45 instead of ode89 right?
Because when we try to solve with ode89 probably it won't plot, I tried with ode45 it works!!
Let me know your views on this!!
Star Strider
Star Strider 2022-9-28
I just wanted to see what the higher order integrator could do. Use whatever integrator you want.

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