Solution
= Solution
The <integrating factor> for this <linear ordinary differential equation> is $e^x$. Multiplication gives $(e^xy)'=1$, so $e^xy=x+C$. The <initial condition> sets $C=0$, giving
$$
\boxed{y(x)=xe^{-x}.}
$$
= Solution
The <integrating factor> for this <linear ordinary differential equation> is $e^x$. Multiplication gives $(e^xy)'=1$, so $e^xy=x+C$. The <initial condition> sets $C=0$, giving
$$
\boxed{y(x)=xe^{-x}.}
$$