ans = Empty sym: 0-by-1 error in solving equation

I am trying to solve a equation for a small project but experiencing

syms x

y= (0:1:100)

avd=5

s = 0.25

paco2=40

r= 0.8

hb=14

pb=740

eqn = ((hb*(((((pb-47)*y-paco2/r).^3+150*((pb-47)*y-paco2/r)).^(-1)*23400)+1).^(-1)*1.34)+((pb-47)*y-paco2/r)*0.0031)- (hb*(((x.^3+150*x).^(-1)*23400)+1).^(-1)*1.34+(x*0.0031))==(s/(1-s))*avd

solve(eqn, x)

and get this result

ans =

Empty sym: 0-by-1

Answer 1

[John D'Errico]

So many times I see this mistake made. I can understand where it comes from. But it gets MATLAB (actually solve) confused.

When you define y in advance as a vector, then the symbolic toolbox thinks you have 101 equations, but only the 1 unknown x. Solve now fails. Instead, you need to leave y as an unknown parameter, and try to solve for x as a function of y.

syms x
% y= (0:1:100)   DON'T DO THIS IN ADVANCE!!!!!!!
% instead, leave y as a symbolic parameter. You will subs in that vector at
% the end.
syms y

avd=5;
s = 0.25;
paco2=40;
r= 0.8;
hb=14;
pb=740;
eqn = ((hb*(((((pb-47)*y-paco2/r).^3+150*((pb-47)*y-paco2/r)).^(-1)*23400)+1).^(-1)*1.34)+((pb-47)*y-paco2/r)*0.0031)- (hb*(((x.^3+150*x).^(-1)*23400)+1).^(-1)*1.34+(x*0.0031))==(s/(1-s))*avd

eqn = 

So we have a rather messy expression for x and y together. Before we go any further, it is ALWAYS important to plot everything.

fimplicit(eqn,[-100 100 0 100])

So fimplicit finds some negative solutions for x, and some large positive solutions between 80 and 100, all depending on the value of y.

If y has a known value, we can clear the fractions, and find what is effectively a 4th degree polynomial in x.

xsol = solve(eqn,x,'returnconditions',true)

xsol = struct with fields:
             x: [4×1 sym]
    parameters: [1×0 sym]
    conditions: [4×1 sym]

xsol.x

ans = 

Unfortunately, we cannot yet resolve the roots, until we substitute in for y. So it is only now that we provide the values for y. For example...

vpa(subs(xsol.x,y,2))

ans = 

So, as I said, a negative root, and a large positive root, and two complex roots.

plot(0:100,double(subs(xsol.x(1),y,0:100)))
xlabel y
ylabel x

Note that the abscissa here is the value of y, and the ordinate (y axis) is the computed value of x, for the first root.

Answer 2

[Torsten]

syms x y
Y = 0:1:100;
avd=5;
s = 0.25;
paco2=40;
r= 0.8;
hb=14;
pb=740;
eqn = ((hb*(((((pb-47)*y-paco2/r).^3+150*((pb-47)*y-paco2/r)).^(-1)*23400)+1).^(-1)*1.34)+((pb-47)*y-paco2/r)*0.0031)- (hb*(((x.^3+150*x).^(-1)*23400)+1).^(-1)*1.34+(x*0.0031))-(s/(1-s))*avd==0;
[N,D] = numden(lhs(eqn));
for i=1:numel(Y)
  sol{i} = vpa(root(subs(N,y,Y(i))));
end

Answer 3

[Nikhilesh]

It seems you are trying to iterate over the value of y and solve for each value of x.

It would be beneficial if you can use a for loop which iterate over values of y (1-100) and place the equation inside the for loop.

for y=0:100

eqn = ((hb*(((((pb-47)*y-paco2/r).^3+150*((pb-47)*y-paco2/r)).^(-1)*23400)+1).^(-1)*1.34)+((pb-47)*y-paco2/r)*0.0031)- (hb*(((x.^3+150*x).^(-1)*23400)+1).^(-1)*1.34+(x*0.0031))==(s/(1-s))*avd

 

S=solve(eqn, x)

end