Unable to find explicit solution

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)

[Torsten]

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.

Answer 1

[Yongjian Feng]

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.

[Yongjian Feng]

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]

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.

Answer 2

[Walter Roberson]

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 = 

Answer 3

[Alex Sha]

One solution seems to be:

t: -8.33315732250827