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.