Warning: Explicit solution could not be found.

Greetings, I was trying to solve the expression that is shown below but MatLab returned the warning expressed on the title.

I want to know why this situation happened, thank you for your answer.

s=solve('-exp(-4*x) + (17/3)*( (x*exp(-3*x)) + exp(-3*x) - exp(-2*x) )=0')

Answer 1

[Walter Roberson]

There are a minimum of 7 different solutions to that equality, all of the 7 complex-valued, and none of them analytical in any analysis method that I am familiar with.

You would have more luck with fsolve() to get a (single) (complex) numeric root.

[Walter Roberson]

I've had my system churning away for over an hour attempting to fnd the solutions when the equation is expressed in WhittakerM formulation; there are no hints yet as to whether it will find anything at all or how long it will take.

[Walter Roberson]

I gave up on the processing with WhittakerM a few hours ago, and started exploring via other means.

I found the startling answer that there are 7 numeric solutions to the equation if your calculation is done with up to 40 digits of working precision, but that if you increase your working precision to 50 or more digits, then only 2 numeric solutions will be found.

To extended digits, the two numeric solutions are

.174944337070096338714467322880408873334791929863861571984160857969475638744 +/- .500663404977444456391555945642612329322605586182808265694813778410392379199*i

where i is the imaginary unit, sqrt(-1)