$(1$ point$)$ The differential equation

$x^2\frac{d^{2}y}{d{x}^2}-7x\frac{dy}{dx}+16y=0$

has $x^{4}as$ a solution.

Applying reduction order $we$ set $y_2=u{x}^4.$

Then $(using$ the prime notation for the derivatives$)$

$y_2^{\text{'}}=$

$y_2^{\text{'}\text{'}}=$

$So,$ plugging $y_2$ into the left side $of$ the differential equation,

and reducing, $we$ get

$x^2{y}_2^{\text{'}\text{'}}-7x{y}_2^{\text{'}}+16y_2=$