Often a differential equation with variable coefficients,

$y^{\text{'}\text{'}}p(t)y^{\text{'}}q(t)y=0$

can be transformed into an equation with constant coefficients by a change of the independent variable. Let

$x=u(t)={\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(q(t){)}^{\frac{1}{2}}dt$

with $q(t)>0,$ be the new independent variable. If the function

$H=\frac{q^{\text{'}}(t)2p(t)q(t)}{2(q(t){)}^{\frac{3}{2}}}$

is a constant, then $($i$)$ can be transformed into an equation with constant coefficients by a change of the independent variable.

Consider the differential equation $y^{\text{'}\text{'}}9t{y}^{\text{'}}{t}^{2}y=0.$ Calculate $H$ using the formula above, and then determine whether it is possible to transform the differential equation into one with constant coefficients using this method.