# I need to solve this D. E. (( plz help ) #2

• Jun 28th 2009, 05:26 AM
amro05
I need to solve this D. E. (( plz help ) #2
• Jun 28th 2009, 06:05 AM
shawsend
Suppose you had \$\displaystyle x-e^x=c\$ and you know that if you can put it into the form \$\displaystyle k=ge^{g}\$, then you can take the Lambert W function of both sides and obtain \$\displaystyle g=W(k)\$. So, can you get \$\displaystyle x-e^x=c\$ into the form \$\displaystyle -(x-c)e^{-(x-c)}=-e^{c}\$ and then taking the W function of both sides get \$\displaystyle -(x-c)=W(-e^{c})\$. Alright then, now do it with \$\displaystyle y'\$, isolate \$\displaystyle y'\$, and then integrate.

. . . oh yeah . . . end special function discrimination: Equal rights for special functions!

. . . same dif with the other one too. Pretty sure anyway, haven't worked it out and checked it though.
• Jun 28th 2009, 02:28 PM
amro05
Quote:

Originally Posted by shawsend
Suppose you had \$\displaystyle x-e^x=c\$ and you know that if you can put it into the form \$\displaystyle k=ge^{g}\$, then you can take the Lambert W function of both sides and obtain \$\displaystyle g=W(k)\$. So, can you get \$\displaystyle x-e^x=c\$ into the form \$\displaystyle -(x-c)e^{-(x-c)}=-e^{c}\$ and then taking the W function of both sides get \$\displaystyle -(x-c)=W(-e^{c})\$. Alright then, now do it with \$\displaystyle y'\$, isolate \$\displaystyle y'\$, and then integrate.

. . . oh yeah . . . end special function discrimination: Equal rights for special functions!

. . . same dif with the other one too. Pretty sure anyway, haven't worked it out and checked it though.

thnx alout my frind
i'll try it and came back to you