cannot find explicit solution symbolic equation

Hi!

I have a an equation with symbolics characters, and i want an expression for one of them ( lamb1 in the present case) but when i use the " solve(t==0,lamb1)" anyway i tried, i can't solve it! It says : "Warning: Cannot find explicit solution. > In solve (line 316)"

my vector t is : ( for the equation t=0 )

t =

                                                                                                                                       0;

 (sin(theta)*(2*lamb3^(beta - 1)*nu - (2*nu*(lamb1*lamb3^2)^(beta/3))/lamb3 + 2*kappa*lamb1*lamb3*(lamb1*lamb3^2 - 1)^(gamma - 1)))/pho0;

 (cos(theta)*(2*lamb3^(beta - 1)*nu - (2*nu*(lamb1*lamb3^2)^(beta/3))/lamb3 + 2*kappa*lamb1*lamb3*(lamb1*lamb3^2 - 1)^(gamma - 1)))/pho0;

So it's not quiet simple. Is there something wrong in what i do ?

Any idea to solve it ? Thank you !

[John D'Errico]

Sorry. It is simply never going to be possible to do what you want. It is trivial to write down a set of equations for which no analytical solution will ever be possible. Just wanting it to work is not sufficient.

[Boris Huljak]

Okay, i was wondering if the problem was from matlab or from my equations ! Thanks for the answer

Answer 1

[Roger Stafford]

You have what appears to be two equations but only one unknown, namely 'lamb1'. You might try listing 'lamb3' as a second unknown and see what happens. There is no guarantee that 'solve' can solve that either because of the complexity of those equations.

Answer 2

[Walter Roberson]

You have lamb1 to the power of the unknown parameter (gamma - 1) . In order to solve that for an explicit solution, there would have to be a closed form method of solving all polynomials of all degrees -- for example, gamma might be 148 so you would need a closed form formula able to explicitly solve polynomials of degree (148-1) = 147. And the formula would have to be valid for all possible integer powers, and for all possible floating point powers as well. It has been proven (Able-Ruffini Theorem) that no such closed formula can possibly exist for polynomials of degree 5 or higher. It is therefore impossible to find an explicit solution to this equation.