Help solving 2 ODEs

W(0)=0; W(f)=2.8; d(P)/d(W)=((-0.3743)/(2*P))*(1-(0.15*X)); P(0)=1; d(X)/d(W)=0.5*((0.08*(0.75*(1-X)))/(1-(0.15*X))); X(0)=0; Trying to solve these two ODEs

Answer 1

[Star Strider]

Try this:

PX_ODE = @(W,PX) [((-0.3743)./(2*PX(1))).*(1-(0.15*PX(2))); 0.5*((0.08*(0.75*(1-PX(2))))./(1-(0.15*PX(2))))];

[W,PX] = ode15s(PX_ODE, [0, 2.8], [1; 0]);

figure
plot(W, PX)
grid

Here ‘P’ is ‘PX(1)’, ‘X’ is ‘PX(2)’. The system encounters a singularity at 2.67, and the integration stops.

[Kurt]

Is there another way to better show both equations

[Star Strider]

Show them in what sense?

Plotting them is the only way I can think of.

[Kurt]

I mean to keep them in their original forms

[Kurt]

I was trying to do it this way, syms P(W) X(W) eqn1 = diff(P, W) == ((-0.3743)/(2*P))*(1-(0.15*X)); eqn2 = diff(X, W) == (0.5*((0.08*(0.75*(1-X)))/(1-(0.15*X))));

[odes, vars] = odeToVectorField(eqn1, eqn2); fun = matlabFunction(odes,'Vars',{'t','Y'}); X0(0) = [0, 0]; tspan = [0, 2.8]; [t, sol] = ode45(fun,tspan,x0);

P = sol(:,2); X = sol(:,1);

[Star Strider]

That certainly works, although ‘P(0)’ cannot be zero. If ‘X(0)’ is greater than 1, the system will integrate out to 2.8.

Also, ‘fun’ is essentially the same as my code, and the result is the same. (The system is ‘stiff’, so ode15s or another stiff solver is more appropriate.)