Unable to find explicit solution

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Berkay Can Tuncel
Berkay Can Tuncel on 19 Jan 2022
Commented: Yongjian Feng on 20 Jan 2022
Hello,
I am trying to solve an equation for one variable but I get this error message:
Warning: Unable to find explicit solution. For options, see help.
> In sym/solve (line 317)
In untitled (line 15)
sol =
Empty sym: 0-by-1
>>
I searched but could'nt find any solution. I couldn't even understand what the problem is. You can see my code below.
Thanks in advance.
syms t
b=2*t+14.3;
w=3*t+21.45;
A=(w*b)-(w-t)*(b-2*t);
rc=(w*b)*450-(w-t)*(b-2*t)*(450+t/2)/A;
rn=A/(b*log((450-w/2+t)/(450-w/2))+2*w*log((450+w/2)/(450-w/2+t)));
E=rc-rn;
ro=450+w/2;
ri=450-w/2;
Ay=-40260.604300;
M1=56124.523326;
sol=solve((Ay/A)+(M1*(ro-rn))/(A*E*ro)==116, t)
  1 Comment
Torsten
Torsten on 19 Jan 2022
Edited: Torsten on 19 Jan 2022
Not all equations can explicitly be solved.
Use "vpasolve" instead of "solve".
If this doesn't yield a result, plot
(Ay/A)+(M1*(ro-rn))/(A*E*ro)-116
for a certain t-interval to see whether a zero really exists.

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Answers (3)

Yongjian Feng
Yongjian Feng on 19 Jan 2022
This equation might not even have a solution. Try to plot it:
syms t
b=2*t+14.3;
w=3*t+21.45;
A=(w*b)-(w-t)*(b-2*t);
rc=(w*b)*450-(w-t)*(b-2*t)*(450+t/2)/A;
rn=A/(b*log((450-w/2+t)/(450-w/2))+2*w*log((450+w/2)/(450-w/2+t)));
E=rc-rn;
ro=450+w/2;
ri=450-w/2;
Ay=-40260.604300;
M1=56124.523326;
x = 1:100;
y = feval(matlabFunction((Ay/A)+(M1*(ro-rn))/(A*E*ro)), x);
plot(x, y)
It looks like when t goes up, (Ay/A)+(M1*(ro-rn))/(A*E*ro)) only goes up from negative to 0. Not sure it will ever reach 116.
  2 Comments
Yongjian Feng
Yongjian Feng on 19 Jan 2022
Try vpasolve as recommended by Torsten above, your equation results in empty solution. Most likely there is not solution for it.
If you plot, you can see (Ay/A)+(M1*(ro-rn))/(A*E*ro)) is always negative. It might never reach 116 as you want.
sol=vpasolve((Ay/A)+(M1*(ro-rn))/(A*E*ro)==0, t) % this gives empty solution. This equation never reaches positive
sol=vpasolve((Ay/A)+(M1*(ro-rn))/(A*E*ro)==-1, t) % this gives 77.287
Yongjian Feng
Yongjian Feng on 20 Jan 2022
Walter is right. I forgot about t<0 range.
If you plot -100:100, you can see most likely there shall be only one solution.

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Walter Roberson
Walter Roberson on 19 Jan 2022
Edited: Walter Roberson on 19 Jan 2022
If you look carefully at the graph, you can see a couple of discontinuities at negative t values.
At first I thought it was a simple case of the system having non-zero imaginary components in some ranges, but it turns out that there are some steep +/- infinities being generated -- and each of those is an opportunity for a solution.
I saw at least one other candidate stretch for a solution between t = 0 and t = -10
syms t
b=2*t+14.3;
w=3*t+21.45;
A=(w*b)-(w-t)*(b-2*t);
rc=(w*b)*450-(w-t)*(b-2*t)*(450+t/2)/A;
rn=A/(b*log((450-w/2+t)/(450-w/2))+2*w*log((450+w/2)/(450-w/2+t)));
E=rc-rn;
ro=450+w/2;
ri=450-w/2;
Ay=-40260.604300;
M1=56124.523326;
eqn = (Ay/A)+(M1*(ro-rn))/(A*E*ro) == 116
eqn = 
sol=solve(eqn, t)
Warning: Unable to find explicit solution. For options, see help.
sol = Empty sym: 0-by-1
string(lhs(eqn) - rhs(eqn))
ans = "5533375321142303/(137438953472*((143*t)/5 - (2*t + 143/10)*(3*t + 429/20) + 61347/200)) - ((23141087250120879*t)/274877906944 + (7713695750040293*((143*t)/5 - (2*t + 143/10)*(3*t + 429/20) + 61347/200))/(137438953472*(log((t/2 - 17571/40)/((3*t)/2 - 17571/40))*(2*t + 143/10) + log(-((3*t)/2 + 18429/40)/(t/2 - 17571/40))*(6*t + 429/10))) + 142155698977492559697/5497558138880)/(((3*t)/2 + 18429/40)*(((143*t)/5 - (2*t + 143/10)*(3*t + 429/20) + 61347/200)/(log((t/2 - 17571/40)/((3*t)/2 - 17571/40))*(2*t + 143/10) + log(-((3*t)/2 + 18429/40)/(t/2 - 17571/40))*(6*t + 429/10)) + 450*(2*t + 143/10)*(3*t + 429/20) + ((t/2 + 450)*((143*t)/5 + 61347/200))/((143*t)/5 - (2*t + 143/10)*(3*t + 429/20) + 61347/200))*((143*t)/5 - (2*t + 143/10)*(3*t + 429/20) + 61347/200)) - 116"
vpasolve(eqn, [-7.985, -7.98])
ans = 

Alex Sha
Alex Sha on 20 Jan 2022
One solution seems to be:
t: -8.33315732250827

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