solving e^x=5x+1

Printable View

October 28th 2012, 05:55 AM
narjsingh

solving e^x=5x+1

solving
e^x=5x+1
thanks
October 28th 2012, 06:12 AM
Kyood

Re: solving e^x=5x+1

there is no exact solution for power-algebric equation
October 28th 2012, 06:43 AM
skeeter

Re: solving e^x=5x+1

Quote:

Originally Posted by narjsingh

solving e^x=5x+1

one solution determined by "observation" is ...

$x = 0$

the other solution can be approximated using technology ...

$x \approx 2.6603991$
October 28th 2012, 07:59 AM
JJacquelin

Re: solving e^x=5x+1

The non-evident root cannot be expressed analyticaly with the combination of a finite number of usual functions.
It can be erxpressed with infinite series (complicated, not useful in practice)
Usally, this kind of equation is solved thanks to numerical computation.
The root can be expressed on a closed form thanks to the Lambert W function :
x = -W(X) where X = -(exp(-1/5)-1)/5
October 28th 2012, 09:36 AM
Kyood

Re: solving e^x=5x+1

Quote:

Originally Posted by skeeter

one solution determined by "observation" is ...

$x = 0$

the other solution can be approximated using technology ...

$x \approx 2.6603991$

In this case, It is ok, but in general it is diffecult to solve such equation directly
for example : solve : e^x=x+2
October 28th 2012, 10:27 AM
JJacquelin

Re: solving e^x=5x+1

Quote:

Originally Posted by Kyood

In this case, It is ok, but in general it is diffecult to solve such equation directly
for example : solve : e^x=x+2

solve exp(x)=x+2 for x - Wolfram|Alpha
October 28th 2012, 11:45 AM
skeeter

Re: solving e^x=5x+1

Quote:

Originally Posted by Kyood

In this case, It is ok, but in general it is diffecult to solve such equation directly
for example : solve : e^x=x+2

I'm pleased that my solution meets your approval ... in "this case".
October 28th 2012, 12:41 PM
Kyood

Re: solving e^x=5x+1

Very nice, skeeter,
you used a special function W(x) which consedered as an approximate solutuion.
October 28th 2012, 01:10 PM
skeeter

Re: solving e^x=5x+1

Quote:

Originally Posted by Kyood

Very nice, skeeter,
you used a special function W(x) which consedered as an approximate solutuion.

no ... I just solved $e^x - 5x - 1 = 0$ with a calculator.
October 29th 2012, 06:28 AM
divyaprashanth07

Re: solving e^x=5x+1

$\int_{0}^{\pi}\frac{x^{4}\left(1-x\right)^{4}}{1+x^{2}}dx =\frac{22}{7}-\pi <br />$
October 29th 2012, 03:40 PM
skeeter

Re: solving e^x=5x+1

Quote:

Originally Posted by divyaprashanth07

$\int_{0}^{\pi}\frac{x^{4}\left(1-x\right)^{4}}{1+x^{2}}dx =\frac{22}{7}-\pi$

... what does this incorrectly evaluated definite integral have to do with this thread?