# How to solve non linear equation for one variable?

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Farhan Ashraf on 24 Apr 2018
Commented: Farhan Ashraf on 24 Apr 2018
Hi, I am trying to solve a non-linear equation for one variable but it's not working. Can somebody help me in this regards? your help would be highly appreciated. Thanks
if
temp=[24 78 139 194 297 397];
yieldstress=[45 36 37 33 30 28];
syms DD positive
solve((6.046.*sqrt(DD))./(1e6)+(9.79.*(1-((-4.7872e-5.*temp).*(log(6.667e-4./(286.*sqrt(DD))))).^(2/3)).^(3/2)).*(3.06) == yieldstress);
end

njj1 on 24 Apr 2018
Edited: njj1 on 24 Apr 2018
If you want to solve for multiple values of temp and yieldstress, you will have to use a for loop.
for i=1:numel(temp)
for j=1:numel(yieldstress)
out{i,j} = solve((6.046.*sqrt(DD))./(1e6)+(9.79.*(1-((-4.7872e-5.*temp(i)).*(log(6.667e-4./(286.*sqrt(DD))))).^(2/3)).^(3/2)).*(3.06) == yieldstress(j));
end
end
The output variable "out" contains the values of DD that solve the equations as symbolic numbers (so long as the equation can be solved), and these can be evaluated using the command eval().

Farhan Ashraf on 24 Apr 2018
Now, Matlab is giving an error, specify a variable for which you solve. I introduce DD at the end of out{i,j} command. still same error is coming
njj1 on 24 Apr 2018

If you type in the code exactly as I have then it should work. It will take a while but it should work.

```for i=1:numel(temp)
for j=1:numel(yieldstress)
out{i,j} = solve((6.046.*sqrt(DD))./(1e6)+(9.79.*(1-((-4.7872e-5.*temp(i)).*(log(6.667e-4./(286.*sqrt(DD))))).^(2/3)).^(3/2)).*(3.06) == yieldstress(j));
dd(i,j) = eval(out{i,j}); %DO NOT put DD here
end
end
```

FYI, I've run this code for the first few values of temp and yieldstress that you posted above, and Matlab is not able to find an explicit solution.

Farhan Ashraf on 24 Apr 2018
what this error mean: A null assignment can have only one non-colon index? can you please guide?

Torsten on 24 Apr 2018
The left-hand side of your equation (6.046.*sqrt(...)...) is a scalar, the right-hand side (yieldstress) is a vector. This is not compatible.
Best wishes
Torsten.

#### 1 Comment

Farhan Ashraf on 24 Apr 2018
Actually I want to calculate DD for each value of yieldstress and temp. Can you please suggest me something?