Solution
= Solution
Writing $v=y-1$ turns the <first-order linear differential equation> into $v'=v$. Its general solution is $v=Ce^x$, so $y=1+Ce^x$. The <initial condition> gives $C=-1$, hence
$$
y(x)=1-e^x,\qquad \boxed{y(1)=1-e}.
$$
= Solution
Writing $v=y-1$ turns the <first-order linear differential equation> into $v'=v$. Its general solution is $v=Ce^x$, so $y=1+Ce^x$. The <initial condition> gives $C=-1$, hence
$$
y(x)=1-e^x,\qquad \boxed{y(1)=1-e}.
$$