Question

$$\frac { d ^ { 2 } y } { d x ^ { 2 } } - 3 \frac { d y } { d x } - 10 y = x ^ { 2 }$$

Solve for x (complex solution)

$x=-i\sqrt{10y}$
$x=i\sqrt{10y}$

Solve for x

$x=\sqrt{-10y}$
$x=-\sqrt{-10y}\text{, }y\leq 0$

Solve for y

$y=-\frac{x^{2}}{10}$