by Guest » Tue Oct 12, 2021 4:43 pm
Since this has been here awhile, I would solve it by writing the equation as
[tex]\frac{dy}{dx}= e^{-y}[/tex].
Separating the values, which the OP did not want to do, [tex]e^ydy= dx[/tex]. Integrating,
[tex]e^y= x+ c[/tex].
Since y(0)= 0, [tex]e^0= 1= 0+ c[/tex] so c=1 so [tex]e^y= x+ 1[/tex].
Then [tex]e^{y(0.5)}= 0.5+ 1= 3/2[/tex].
[tex]y(0.5)= ln(3/2)[/tex].