solving

e^x=5x+1

thanks

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- Oct 28th 2012, 05:55 AMnarjsinghsolving e^x=5x+1
solving

e^x=5x+1

thanks - Oct 28th 2012, 06:12 AMKyoodRe: solving e^x=5x+1
there is no exact solution for power-algebric equation

- Oct 28th 2012, 06:43 AMskeeterRe: solving e^x=5x+1
- Oct 28th 2012, 07:59 AMJJacquelinRe: 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 - Oct 28th 2012, 09:36 AMKyoodRe: solving e^x=5x+1
- Oct 28th 2012, 10:27 AMJJacquelinRe: solving e^x=5x+1
- Oct 28th 2012, 11:45 AMskeeterRe: solving e^x=5x+1
- Oct 28th 2012, 12:41 PMKyoodRe: solving e^x=5x+1
Very nice, skeeter,

you used a special function W(x) which consedered as an approximate solutuion. - Oct 28th 2012, 01:10 PMskeeterRe: solving e^x=5x+1
- Oct 29th 2012, 06:28 AMdivyaprashanth07Re: solving e^x=5x+1
$\displaystyle \int_{0}^{\pi}\frac{x^{4}\left(1-x\right)^{4}}{1+x^{2}}dx =\frac{22}{7}-\pi

$ - Oct 29th 2012, 03:40 PMskeeterRe: solving e^x=5x+1