Real solution for a variable in an equation

Hi all, I have an equation and I want to find the real solution (c>0), for eqn, but this code doesn't work. Could you please tell me what is wrong in the below code that I wrote. Thanks in advance for any help

V_plc=0.19;

Kf=0.18;

Kc=0.1;

Kp=0.15;

Kb=0.4;

Kh=0.05;

tau=0.18;

Ktau=0.045;

Vs=0.002;

Kbar=1.5e-5;

Ks=0.1;

Vpm=1.59e-4;

Kpm=0.15;

alpha0=6.81e-6;

alpha1=2.27e-5;

Kce=7;

delta=0.1;

gamma=5.5;

Kplc=0.055;

k_i=2;

ct=0.07;

syms c

p=(V_plc.*c.^2/(c.^2+Kplc.^2))./k_i;

h=Kh.^4./(Kh.^4+c.^4);

Po=((p.^2)*(c.^4).*h)./((p.^2).*(c.^4).*h.*(1+Kb)+Kb.*Kp.^2*(Kc.^4+c.^4-((c.^4*Kh.^4)./(c.^4+Kh.^4))));

jpm=Vpm.*(c.^2/(c.^2+Kpm.^2));

eqn=(((alpha1.*Kce.^4)./(jpm-alpha0))-Kce.^4).^(1/4)-((Vs.*c.^2)./(Kf.*Po.*(c.^2+Ks.^2)))-c==0;

S = solve(eqn,c,'Real',true)

Answer 1

[Chunru]

V_plc=0.19;
Kf=0.18;
Kc=0.1;
Kp=0.15;
Kb=0.4;
Kh=0.05;
tau=0.18;
Ktau=0.045;
Vs=0.002;
Kbar=1.5e-5;
Ks=0.1;
Vpm=1.59e-4;
Kpm=0.15;
alpha0=6.81e-6;
alpha1=2.27e-5;
Kce=7;
delta=0.1;
gamma=5.5;
Kplc=0.055;
k_i=2;
ct=0.07;
syms c
p=(V_plc.*c.^2/(c.^2+Kplc.^2))./k_i;
h=Kh.^4./(Kh.^4+c.^4);
Po=((p.^2)*(c.^4).*h)./((p.^2).*(c.^4).*h.*(1+Kb)+Kb.*Kp.^2*(Kc.^4+c.^4-((c.^4*Kh.^4)./(c.^4+Kh.^4))));
jpm=Vpm.*(c.^2/(c.^2+Kpm.^2));
% eqn=(((alpha1.*Kce.^4)./(jpm-alpha0))-Kce.^4).^(1/4)-((Vs.*c.^2)./(Kf.*Po.*(c.^2+Ks.^2)))-c==0;
% S = solve(eqn,c,'Real',true)

% The function you specified is a complex function that has no solution.
% Check out abs(f) which never reaches to 0.

f1= (((alpha1.*Kce.^4)./(jpm-alpha0))-Kce.^4).^(1/4)-((Vs.*c.^2)./(Kf.*Po.*(c.^2+Ks.^2)))-c;
fplot(real(f1), [0 1]); hold on
fplot(imag(f1), [0 1])
fplot(abs(f1), [0 1])
ylim([-1 1]*5)
xlim([0 0.4])

[Chunru]

But it is proved that your problem has no real solution.

[M]

Yeah that's true...