To solve a second order differential equation with initial conditions using matrix method

Consider a system governed by a second ODE y''+6y'+5y = 8*exp(-t) with the initial conditions y(0)=y'(0)=0, I need a matlab code to solve the equations using matrix methods

[madhan ravi]

Is it your homework ? What did you try so far? https://www.mathworks.com/help/symbolic/massmatrixform.html

Answer 1

[Ameer Hamza]

Try the following code using ode45 (a numerical solver). Also, see this example from the documentation: https://www.mathworks.com/help/matlab/ref/ode45.html#bu3uj8b

[t, y] = ode45(@odeFun, [0 10], [0; 0]);
plot(t, y, 'o-')

function dydt = odeFun(t, y)
    A = [0 1;
         -5 -6];
    B = [0; 8];
    u = exp(-t);
    dydt = A*y + B*u;
end

Alternative method using symbolic toolbox

syms y(t)

eq = diff(y, 2) + 6*diff(y, 1) + 5*y == 8*exp(-t);
odeFun = matlabFunction(odeToVectorField(eq), 'Vars', {'t', 'Y'});
ode45(odeFun, [0 10], [0; 0])