Solving 2 differential equations simultaneously

I am trying to solve 2 equations with 2 variables.

Eq 1: w''(t)=-0.03.w'(t)/r(t)

Eq 2: w'(t)=-0.005.w(t)/r(t)

w(0)=0.6, w'(0) = 0.001, r(0)=12

I could not find a way to solve the 2 equations using ode45.

 tspan=[0 500];
 w0=0.6;
 r0=12;
 [t,w,r] = ode45(@angvel, tspan, w0,r0);
 function dwdt = angvel(t,w,r)
        dwdt = -0.005*w/(0.01*r);
 end

The error when I try to solve Eq1 is insufficient inputs. Where am I going wrong? Please advise. Thanks!

[Aquatris]

I might be wrong but the initial conditions do not seem to satisfy the equation 2. Are you sure these are the equations?

[BHAGYASHREE WAGHULE]

I'm actually researching. I don't know for sure if the initial condition is correct. My advisor wants me to try different valies for w'. The equation is correct, the initial condition for w' is not known to me at least. And rate of change of r(t) is constant, but r(t) changes.

Answer 1

[Diwakar Ravichandran]

Hi Bhagyashree,

As I was going through your equations, I noticed that when you substitute equation 2 in equation 1 we get,

w"(t) = (1.5*10^-4)*[w(t)/r^2(t)];

which is a single equation with 2 unknown variables and hence it cannot be solved using conventional methods. You would need to gather more information about the unknowns and their behavior to solve this equation.

Hope this helps,

Cheers!