How to solve the following system of ODE's?

I'm not sure where to start even. I thought this could be done using ode15 or ode23 to solve a system of differential algebraic equations, but I'm stuck at the part where I need to define the function describing the equations. How do I account for the derivative of the other variable in one equation?

Answer 1

[Aquatris]

Here is a code;

 syms Po(t) Pi(t)

 co = 5;
 cl = 2;
 pes = 2;
 pon = 10;
 peu = 7;
 R = 34;
 cs = 23;
 cb = 10;
 Qa = 2;
 ct = 12;
 Qu = 15;  

 ode1 = (co+cl)*diff(Po) - cl*diff(Pi) == (pes-pon)/R;
 ode2 = (co+cs+cb)*diff(Pi) - cl*diff(Po) == Qa + ct*(Pi-peu)-Qu;
 odes = [ode1; ode2];
 S = dsolve(odes)