ODEs

ode23('0',[0 10],1)
ode23(@(t,y) 0,[0 10],1)
ode23(@(t,y) t,[0 10],1)
ode23(@(t,y) y,[0 10],1), grid
ode23(@(t,y) -y,[0 10],1), grid
ode23(@(t,y) 1/(1-3.*t),[0 10],1), grid


ode23(@(t,y) [y(2); -y(1)], [0 3*pi], [0;1]), grid
[t y] = ode23(@(t,y) [y(2); -y(1)], [0 2*pi], [0;1]);
plot(y(:,1), y(:,2), 'o-'), grid, axis equal
[t y] = ode23(@(t,y) [y(2); -y(1)], [0 2*pi], [0;1], odeset('Refine', 2));

doc odeset
odeset

[t y] = ode45(@(t,y) [y(2); -y(1)], [0 2*pi], [0;1]);
plot(y(:,1), y(:,2), 'o-'), axis equal, grid
[t y] = ode45(@(t,y) [y(2); -y(1)], [0 2*pi], [0;1], odeset('Refine', 1));

syms y(x)
dsolve(diff(y(x),x) == y*x)
ys = dsolve(diff(y(x),x) == y*x, y(1)==1)
fplot(ys)

eqn2 = diff(y,x,x) + 8*diff(y,x)+2*y == cos(x)
dsolve(eqn2)

F = @(t,y) -100*y + 100*t +1
ode45(F, [0 1], 1)
ode15s(F, [0 10], 1)

expgui
ncmgui