How to use ode45 with a time dependant second order differential equation

Hello,

I have the below code for a second order ordinary differential equation. In this, the value of D depends on y (as shown by the commented line). I see from the Matlab help file for ode45, how such an equation be solved for a first order. But I don't know how to do it for a second order equation. Could you please help? Thank you.

syms h(t)

A=10*diff(h, 2);
B=8 * diff(h) ;
C=10 * h ; 
%D=interp1(E(:,1),E(:,2),y)
D=2; %[
 
[V] = odeToVectorField(A == (D-C-B));
M = matlabFunction(V,'vars', {'t','Y'});
sol = ode45(M,[0 10],[0 0]);
fplot(@(x)deval(sol,x,1), [0, 10]);

Answer 1

[Alan Stevens]

Turn your second order equation into two simultaneous first order equations.

[curiously learning]

Thank you for the suggestion. That is where I am struggling. To convert, one has to use a odetovectorfield, and I don't know how to use it in this context. Could you perhaps give an example?

[Alan Stevens]

If you are interested only in numerical results you don't need any symbolic stuff at all.

With an equation like d^2y/dt^2 + a*dy/dt + b*y = 0, you can turn that into two first order equations bysetting

dy/dt = v

dv/dt = -a*v - b*y

Do

doc ode45

for more details.