MATLAB: Solve for symbolic initial conditions

dsolvesolveSymbolic Math Toolbox

A second order mass, damper, spring system can be solved from
syms h(t) m c k h0 dh0 C10 C11
Dh=diff(h(t),t);
eqs = m*diff(h(t), t, t) == -c*Dh-k*h(t);
sol=dsolve(eqs);
h0=subs(sol,t,0);
dh0=subs(diff(sol,t),t,0);
How to rewrite the solution (sol) using the initial condtions (h0, dh0)? I am trying to determine the transition matrix, given h, dh at time 0, find the transition matrix, X, to give h, dh at later time t. I'm looking for a solution like
ic=solve({h0,dh0},{C10, C11})

Best Answer

I’m not certain what you’re asking. It’s easy enough to incorporate the initial conditions in your dsolve call, and it’s in the documentation:
syms h(t) m c k h0 dh0 C10 C11
Dh(t)=diff(h(t),t);
eqs = m*diff(h(t), t, t) == -c*Dh-k*h(t);
sol=dsolve(eqs, h(0)==h0, Dh(0)==dh0);
You can also do the integration numerically with ode45, and probably more easily, especially if you use the odeToVectorField function to create the system of first-order ODEs the numeric ODE solvers require. If you do a numeric integration, do not include the initial conditions in your differential equations. Specify them in the ode45 call instead.
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