Solving System of Differential Equations

syms I so s(t) as(t) mo m(t) am(t) im(t) img(t) po p(t) kcp t a(t) ao am(t) kca kona koffa konm koffm kong koffg ksig g(t) go
eqn1 = diff(s) == (-kona*s*a)+koffa*as;
eqn2 = diff(m) == -konm*m*a+koffm*a*m-konm*I*m+koffm*im; eqn3 = diff(g) == -kong*im*g+koffg*img; eqn4 = diff(img) == kong*im*g-koffg*img; eqn5 = diff(p) == ksig*img-kcp;
I= 1; so=1; mo=1;go=1; po=1; kcp=1; ao=1; kca=1; kona=1; koffa=1; konm=1; koffm=1; kong=1; koffg=1; ksig=1; eqn6= so==s+as; eqn7= mo==m+am+im+img; eqn8= go==g+img; eqn9= po==p+kcp*t; eqn10= a==(a-am-as)/((kca*t)+1);
S = dsolve(eqn5, eqn2, eqn3, eqn4,eqn5,eqn6,eqn7,eqn8,eqn9,eqn10)

Error using mupadengine/feval (line 163)
Invalid equation or initial condition.

Error in dsolve>mupadDsolve (line 336)
T = feval(symengine,'symobj::dsolve',sys,x,options);

Error in dsolve (line 193)
sol = mupadDsolve(args, options);

I am trying to solve a system of differential equations, but I get these errors which I'm not sure how to fix. Thanks for the help!

[Walter Roberson]

 dsolve(eqn5, eqn2, eqn3, eqn4,eqn5,eqn6,eqn7,eqn8,eqn9,eqn10)

repeats eqn5 and does not mention eqn1

[Pablo Estuardo]

same probleme here..

syms  u(t) v(t) f taux tauy Hm rho R u0 v0 
du = diff(u);
dv = diff(v);
DE = [du - f*v == taux/(Hm*rho) - R*u;  dv + f*u == tauy/(Hm*rho) - R*v]
Soln = dsolve(DE, u(0)==u0, v(0)==v0)

Error using mupadengine/feval (line 163)

The equations are invalid.

Error in dsolve>mupadDsolve (line 336)

T = feval(symengine,'symobj::dsolve',sys,x,options);

Error in dsolve (line 193)

sol = mupadDsolve(args, options);

Answer 1

[Walter Roberson]

eqn10 is of the form

a(t) == -(am(t) - a(t) + as(t))/(t + 1)

Even if you simplify to

a(t) = -(am(t) + as(t))/t

you have the problem that this is not a differential equation and is not an initial condition.

You eqn6, eqn7, eqn8, and eqn9 are of the form

constant == sum of functions of t

Those are not initial conditions or differential equations either.

If the line

    a(t) == -(am(t) - a(t) + as(t))/(t + 1)

exists for the purpose of defining a(t) for use in the other equations, then instead of presenting it as a condition or equation, you have to substitute it into the other equations (preferably after reducing it to -(am(t) + as(t))/t )