Solve the Lotka-Volterra differential equation system with the Hamiltonian function

I have the following code where I would like to solve the system with dsolve but somehow I get the following error:

No differential equations found. Specify differential equations by using symbolic functions.

I started to work on optimal control with binary control functions, but I have already stucked in here.

Here's my code:

c0 = 0.5;
c1 = 0.7;

% state equations
syms x0 x1 lambda0 lambda1 w
dx0 = x0-x0*x1-c0*x0*w;
dx1 = -x1+x0*x1-c1*x1*w;

%objective function
syms g;
g = (x0-1)^2+(x1-1)^2;

%hamiltonian function;
syms lambda0 lambda1 H;
H = -g+lambda0*dx0+lambda1*dx1;

%"costate equations" 
dlambda0 = -diff(H,x0);
dlambda1 = -diff(H,x1);

%solve for control w 
dw = diff(H,w);
sol_w = solve(dw,w);

% Substitute w to state equations
dx1 = subs(dx1, w, sol_w);

% convert symbolic objects to strings for using ’dsolve’
eq1 = strcat('dx0=',char(dx0));
eq2 = strcat('dx1=',char(dx1));
eq3 = strcat('dlambda0=',char(dlambda0));
eq4 = strcat('dlambda1=',char(dlambda1));

% HERE IS THE PROBLEM
sol_h = dsolve(eq1,eq2,eq3,eq4)

Thank you for your help !