independent variable shows up as an arrow after using subs

After using subs to replace a variable 'u' in an array H with the time dependent function 'u(t)', the array shows '(t -> u(t)) at every occurrence of u in the array. When I then try to solve this array as a system of ODE's using dsolve, the solver fails saying the system does not seem to be linear. If I manually copy the array into the command window, and remove all occurrences of 't ->', the system is solved normally.

To illustrate,

H1=u^2+w;
H2=u+w^2;

dH1du=diff(H1,u);
dH1dw=diff(H1,w);
dH2du=diff(H2,u);
dH2dw=diff(H2,w);
dH=[(dH1du+dH2du);(dH1dw+dH2dw)]

syms u(t) w(t)
dH=subs(dH,[u,w],[u(t),w(t)])

ode1=diff(u)==dH(1);ode2=diff(w)==dH(2);odes=[ode1;ode2]
uw=dsolve(odes)

gives the output:

dH =

   2*u + 1
   2*w + 1

dH =

   2*(t -> u(t)) + 1
   2*(t -> w(t)) + 1

odes(t) =

   diff(u(t), t) == 2*(t -> u(t)) + 1
   diff(w(t), t) == 2*(t -> w(t)) + 1

Error using mupadengine/feval (line 163)
This system does not seem to be linear.

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

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

Error in matlabwebsitequestion (line 17)
uw=dsolve(odes)

If, instead, I manually replaced the last two lines with the following:

ode1=diff(u)==2*(u(t)) + 1;ode2=diff(w)==2*(w(t)) + 1;odes=[ode1;ode2]
uw=dsolve(odes)

I get the output:

odes(t) =

   diff(u(t), t) == 2*u(t) + 1
   diff(w(t), t) == 2*w(t) + 1

uw = 

      w: [1x1 sym]
      u: [1x1 sym]

Note that I couldn't declare 'syms u(t) w(t)' from the beginning because I need the partial derivatives of H with respect to these two variables, and if I had declared them with their time functionality from the beginning, I get:

Error using sym/diff (line 26)
All arguments, except for the first one, must not be symbolic functions.

Error in matlabwebsitequestion (line 7)
dH1du=diff(H1,u);

Answer 1

[Omanshu Thapliyal]

This is happening because you probably have symbolic variables 'u' and 'v' declared somewhere a priori. When you do

syms u(t) v(t)

it overwrites the already present 'u' and 'v', which are referred to in the expression

dH=[(dH1du+dH2du);(dH1dw+dH2dw)]

Now when you do 'subs', you are replacing the u in u(t) and not the original u.

The correct way to solve the differential equation would be to replace u and w used before the 'subs' call by some dummy variables, say, 'x' and 'y'.