piecewise differential equation in matlab

To solve a piecewise differential equation in MATLAB, the dsolve function can be used along with specifying the piecewise conditions. Here is an example code:

main.m
syms x(t) % defining the symbolic function x(t)
eqn = diff(x,t,2) == -9.81 + piecewise(t<10, 2, t>=10, 0); % defining the piecewise differential equation
Dx = diff(x,t);
cond = [x(0)==0, Dx(0) == 0]; % initial conditions
xSol(t) = dsolve(eqn, cond); % solving the differential equation with initial conditions
fplot(xSol, [0, 15]) % plotting the solution
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In this example, we are solving the differential equation d^2x/dt^2 = -9.81 + 2 (t<10) + 0 (t>=10) subject to initial conditions x(0)=0 and dx/dt(0)=0. The piecewise function is used to define the equation with different values of 2 when t is less than 10, and 0 when t is greater than or equal to 10. The fplot function is used to plot the obtained solution between the time intervals [0, 15].

Note that the syms function is used to define the symbolic function x(t).