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 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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