express ODE without set a m file function

Can someone explain this to me? actually this is part od example in the numerical book

I found example in numerical book about ODE that can formulated by

dx/dt=v

dv/dt=g-cd/m*v*abs(v)

and used a M-fle function to express those system by

function dydt=freefall(t,y,cd,m)

%y(1)=x and y(2)=v

grav=9.81;

dydt=[y(2);grav-cd/m*y(2)*abs(y(2))];

then calculate ODE using ode45

opts=odeset('events',@endevent);

y0=[-200 -20];

[t,y,te,ye]=ode45(@freefall,[0 inf],y0,opts,0.25,68.1);

te,ye

plot(t,-y(:,1),'-',t,y(:,2),'--','LineWidth',2)

legend('Height (m)','Velocity (m/s)')

xlabel('time (s)');

ylabel('x (m) and v (m/s)')

i try to calculate ODE withouy making function m-file to perform ODE as shown below

func=@(dxdt) [dxdt;9.81-0.25/68.1*dxdt*abs(dxdt)];

[t,y,te,ye]=ode45(func,[0 inf],y0,opts);

but it doesn't work. Can anyone explain to me why or it should make a separete function to solde ode using ode45 in matlab?

Answer 1

[Rik]

If you want to replicate the results, you need to replicate the function exactly:

func=@(t,y,cd,m) [y(2);9.81-cd/m*y(2)*abs(y(2))];

Answer 2

[Walter Roberson]

func=@(dxdt) [dxdt(2);9.81-0.25/68.1*dxdt(2)*abs(dxdt(2))]

However you will have problems when 0 is crossed.