For a 2nd order differential equation of the form - y'' + p(t) y' + q(t)y = g(t) with initial conditions - y(to) = yo and y'(to) = y1
We assign x1 = y; x2 = y0
Step 1) First convert 2nd order equation to an equivalent system of 1st order equations.
- Let x1 = y and x2 = y'
Thus,
- x1' = x2
- x2' = -q(t)x1 - p(t)x2 + g(t)
Step 2) Create and save a .m file which will return a vector-valued function
function xp=eg1(t,x)
xp=zeros(2,1);
xp(1)=x(2);
xp(2)=(0.35/13)*x(1)-(0.27/13)*x(2)+(1.2753/13);
end
Step 3) Call the function by using the command -
[t,x]=ode45('eg1',[0,5],[0,0]);
