# exponential equation

sage: solve(exp(-x)+exp(x) == 2,x)
[x == 0]
sage: solve(exp(-2*x)+exp(2*x) == 2,x)
[]

Can tell me anyone why the second equation has no solution?

exponential equation

sage: solve(exp(-x)+exp(x) == 2,x)
[x == 0]
sage: solve(exp(-2*x)+exp(2*x) == 2,x)
[]

Can tell me anyone why the second equation has no solution?

1

I unfortunately don't have time to check why this doesn't work, but the following keyword argument (useful to know in any case) does work:

```
sage: (exp(-2*x)+exp(2*x) == 2).solve(x,to_poly_solve=True)
[x == I*pi*z15]
```

which should be interpreted as saying `z15`

is a free integer variable (hence `z`

). One can also do

```
sage: (exp(-x)+exp(x) == 2).solve(x,to_poly_solve='force')
[x == 2*I*pi*z24]
```

for all possible solutions to the original one. Unfortunately, finding the documentation for this (currently) requires using the method notation instead of functional

```
sage: solve?
```

notation.

Please start posting anonymously - your entry will be published after you log in or create a new account.

Asked: ** 2010-10-02 13:35:11 +0200 **

Seen: **3,360 times**

Last updated: **Oct 02 '10**

exponential equation real solution

Using the solution of equation

Issues with: Solving a polynomial equation with multiple variables

SAGETEX: Howto compute solution of a function

Numerical real solution of derivative

How to get all (numerical) solutions of an equation?

Copyright Sage, 2010. Some rights reserved under creative commons license. Content on this site is licensed under a Creative Commons Attribution Share Alike 3.0 license.

For the record, this question is closely related to http://ask.sagemath.org/question/156/exponential-equation-real-solution