Unable to find explicit solution

Question

Berkay Can Tuncel 2022-1-19

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https://ww2.mathworks.cn/matlabcentral/answers/1632110-unable-to-find-explicit-solution

评论： Yongjian Feng 2022-1-20

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)

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Torsten 2022-1-19

编辑：Torsten 2022-1-19

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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Answer 1

Yongjian Feng 2022-1-19

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在 MATLAB Online 中打开

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.

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Yongjian Feng 2022-1-19

在 MATLAB Online 中打开

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 2022-1-20

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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Answer 2

Walter Roberson 2022-1-19

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https://ww2.mathworks.cn/matlabcentral/answers/1632110-unable-to-find-explicit-solution#answer_877725

编辑：Walter Roberson 2022-1-19

在 MATLAB Online 中打开

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 =