# 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.

Asked: **
2010-10-02 06:35:11 -0500
**

Seen: **1,610 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

roots() returns no real solutions for cubic function

using sage solve for more than 4 variables

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