We study the differential equation
$$y(x) y'(x) = -4x \tag{E}$$
Show that if $f$ is a solution of $(E)$ on an interval $J$, and if $a$ is a nonzero real number, then the function $h$ defined by $h(x) = a f\left(\frac{x}{a}\right)$ is also a solution of $(E)$ on an interval that one will specify.