Solve symbollically a 1st order ODE with non-constante coefficient - dsolve

Hello, I am trying to solve the following ODE:

syms mu(z) theta u_o Kx Ky h z rho w

u_x  = cos(theta)*u_o*(cos(Kx*z)+tan(Kx*h)*sin(Kx*z));
du_x = diff(u_x,z);
eqn1 = diff(mu(z)*du_x,z) == -rho*w^2*u_x;

dsolve(eqn1)

However I get the following error message:

Warning: Unknown functions not appearing in the system are ignored. 
> In symengine
  In mupadengine/evalin (line 102)
  In mupadengine/feval (line 161)
  In dsolve>mupadDsolve (line 336)
  In dsolve (line 194)
  In main (line 68) 
Error using mupadengine/feval (line 166)
The number of arguments is incorrect.

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

Error in dsolve (line 194)
sol = mupadDsolve(args, options);

Error in main (line 68)
dsolve(eqn1)

I would understand a message saying it didn't find the explicit solution, but here I don't know what to make of it.

Does anyone know where this is coming from and what i could try to solve this ODE?

Thank you,

Nicolas

Answer 1

[Star Strider]

When I declare ‘u_x’ as ‘u_x(z)’, (in R2017b) I get:

syms mu(z) theta u_o Kx Ky h z rho w

u_x(z)  = cos(theta)*u_o*(cos(Kx*z)+tan(Kx*h)*sin(Kx*z));
du_x = diff(u_x,z);
eqn1 = diff(mu(z)*du_x,z) == -rho*w^2*u_x;

desol = dsolve(eqn1)

desol =
(rho*w^2 + C2*exp(- log(exp(-Kx*h*2i)*exp(Kx*z*2i) - 1) + Kx*z*1i))/Kx^2

What result do you want?

[Nicolas]

Thanks, I see where it went wrong. I needed to declare u_x(z) instead of just u_x.

[Star Strider]

As always, my pleasure.