Unable to find explicit solution

syms x y

A=(1-sqrt(1-x))^.5*tan((1-sqrt(1-x))^.5*y)

B=(1+sqrt(1-x))^.5*tan((1+sqrt(1-x))^.5*y)

solx=solve(A==B,x)

Hello,

I have this problem here, but when I run the code, it will give me a warning Unable to find explicit solution. I tried also to use vpasolve to solve it numerically but it did not work. Are there any alternatives to solve the problem?

Answer 1

[John D'Errico]

Does a solution exist for EVERY possible function you can write down? (NO.) In fact, it is trivially easy to write down infinitely many sets of equations that have no solution.

syms x y
A=(1-sqrt(1-x))^.5*tan((1-sqrt(1-x))^.5*y);
B=(1+sqrt(1-x))^.5*tan((1+sqrt(1-x))^.5*y);

A - B

ans = 

I'm not sure why you would expect to see an algebraic solution to that problem.

fimplicit(A-B)

Each blue line in that solution is an entire family of solutions to the problem. So, given any value for y, there are infinitely many possible solutions for x, given y. But there will be no simple algebraic solution, nothing nice and simple you can write down.

In general (I said this just the other day too) when you have a variable both inside and outside a trig function, you will never find an analytical solution. (There will surely be some rare counter-examples to that statement, but it is true in general.)

[SAM]

actually, I am trying to find a solution as a counter but it did not work for me either way.

Here is how my original problem looks like, it is actually a geotechnical problem.

where

But my final solution should have this form

sorry I am a beginner in Matlab so that's I am not able to understand how to use it appropriately for my problem, but anyways thank you so much.