Solution
= Solution
Multiplication by $e^y$ gives $d(e^y)/dx=x/\sqrt{1+x^2}$. Integrating and imposing $y(0)=0$ yields $e^y=\sqrt{1+x^2}$. Therefore
$$
\boxed{y=\tfrac12\log(1+x^2),\qquad x\in\mathbb R.}
$$
= Solution
Multiplication by $e^y$ gives $d(e^y)/dx=x/\sqrt{1+x^2}$. Integrating and imposing $y(0)=0$ yields $e^y=\sqrt{1+x^2}$. Therefore
$$
\boxed{y=\tfrac12\log(1+x^2),\qquad x\in\mathbb R.}
$$