third order differential equation with matlab

hi i want to solve third order differential equation with matlab y'''+6y''+28y'+40y= cos (4t) where y(0)=1 , y'(0)=1 , y''(0)=0 thanks in advance

[John D'Errico]

Read the help for the ODE tools. Start with

doc ode45

You might be surprised, and find they teach you to do virtually exactly what you need to do. But if you never read the help, then you ask us to re-write the help docs, just so that you can read what we wrote. That would be silly.

Answer 1

[Star Strider]

If you are using the Symbolic Math Toolbox, solving it is something of a challenge. This is a linear differential equation:

% y''' + 6y'' + 28y' + 40y = cos(4t)
syms s t y(t) Y 
Dy = diff(y);
D2y = diff(y,2);
D3y = diff(y,3);
Eqn = D3y + 6*D2y + 40*y == cos(4*t);
LEqn = laplace(Eqn)
LEqn = subs(LEqn, {laplace(y(t), t, s), subs(diff(y(t), t), t, 0), subs(diff(y(t), t, t), t, 0)},  {Y, 1, 0})
Ysol = solve(LEqn, Y)
Ysol = subs(Ysol, {y(0)}, {1})
Y = vpa(ilaplace(Ysol))

figure
fplot(Y, [0 3*pi])
grid

This seems to be an unstable system, so check it to be certain.

Since this is likely homework, I present this solution because using Laplace transforms in MATLAB to solve differential equations is not as straightforward as it might be. (The dsolve function apparently just gets lost.) I would not expect those who have not previously encountered these problems to be able to deal with them effectively.

Of course, you can always simply cut to the chase and use the odeToVectorField and matlabFunction functions, using the result with the numerical solvers. That is obviously easier.

Your choice.