"Cannot find explicit solution"

Matlab says "Cannot find explicit solution", although I can solve it manually.

The initial equation is below:

And the explicit solution is below:

What is wrong with my code, below?

----------------------------------

>> syms x n b r a

eqn = x*(1+n)==(b/(b+1))*r*(1-a)*x^a ;

solx = solve(eqn, x)

Warning: Cannot find explicit solution. 

> In solve (line 318) 

solx =

Empty sym: 0-by-1

------------------------------------

[Walter Roberson]

Which MATLAB version are you using?

Check to see if eqns is already a logical value even before the solve() call; that happened in older MATLAB releases.

[P J]

Thank you so much for your help.

The version is R2015a (8.5.0.197613) 32 bit (win32) February 12, 2015.

When I put a more simpler equation, such as below, it worked well.

Also, I cleared all of the previous variables in the workspace, using the function "clear all."

---------------------------------------

syms x y z

eqn = x*y+x*z==z^3+y^4+15 ;

solx = solve(eqn, x)

solx =

(y^4 + z^3 + 15)/(y + z)

---------------------------------------

Answer 1

[Star Strider]

Sometimes, you have to lead it gently by the hand:

syms x n b r a 

eqn = x*(1+n)==(b/(b+1))*r*(1-a)*x^a ;

eqn = rewrite(eqn,'log');

solx = solve(eqn, x, 'IgnoreAnalyticConstraints',1)

pretty(solx)

solx =

(-((b + 1)*(n + 1))/(b*r*(a - 1)))^(1/(a - 1))

                         1
                       -----
  /   (b + 1) (n + 1) \a - 1
  | - --------------- |
  \     b r (a - 1)   /

[P J]

Your answer is great help for me !! It worked, when I pasted it to Matlab.

Interestingly, removing the line below also yield the same answer.

eqn = rewrite(eqn,'log');

With your answer, I am able to study Matlab further by searching at Mathworks webpage: http://www.mathworks.com/help/.

[Star Strider]

My pleasure.

Your second result (after removing the rewrite call) is interesting. I got the same results you did before adding the rewrite call. After adding it, I got the correct result. I didn’t experiment with removing it again.

[Trevor Gates]

Hello,

I am having the same problem (i.e. unable to find explicit solution), except that in my case, there are 7 equations (with some being inequalities). Again, I am able to find an explicit solution for 'a' by hand. Is there a similar trick that I can use to help the solve() function to find it? Below is my source code. I am using the Student Version R2010a.

syms a s lambda1 lamdbda2;

obj = log(a);

cons1 = a;

cons2 = s/2 - a;

Lagrange = obj + lambda1*cons1 + lambda2*cons2;

eq1 = [char(diff(Lagrange, a)), '=0'];

eq3 = [char(diff(Lagrange, lambda1)), '>=0'];

eq4 = [char(diff(Lagrange, lambda2)), '>=0'];

eq3a = [char(diff(Lagrange, lambda1)*lambda1), '=0'];

eq4a = [char(diff(Lagrange, lambda2)*lambda2), '=0'];

eq6a = 'lambda1>=0';

eq6b = 'lambda2>=0';

[a_sol] = solve(eq1, eq3, eq4, eq3a, eq4a, eq6a, eq6b, a);

[Walter Roberson]

Trevor, your situation has to do with a MATLAB bug in the old release you are using. The workaround is to call into MuPAD directly.

Answer 2

[Shashank kumar]

Hello i am also having the same problem. The above explain code is not able to solve my problem. If possible please look into it.

syms y k p b c;
eqn= k*p^(1-a)==b*p^(-a)+c;
eqn=rewrite(eqn,'log');
sol=solve(eqn, p, 'IgnoreAnalyticConstraints',1)
pretty(sol)

[Walter Roberson]

There is no analytic solution to that equation.