let be the differential equation $ -y''(x)+x^{4}y(x)-E_{n}y(x)=0 $ with the boundary conditions $ y(0)=0=y(\infty) $

how could i use the shooting method or other numerical method to solve this equation ? , my only idea is to set $ R=10000 $ for example and solve $ y(0)=0=y(R) $

of course i also could made the substitution $ u= \frac{x}{x-1} $ so the new boundary conditions could become $ y(0)=0=y(1) $ but know the differential equation would be singular at the point $ u=1 $