Consider the differential equation

x$2$y$7$xy$+12$y $=0$;$$x$2,$ x$6,(0,$ $).$

Verify that the given functions form a fundamental set of solutions of the differential equation on the indicated interval.

The functions satisfy the differential equation and are linearly independent since

W$($x$2,$ x$6)=$

$2$x

$0$

for

$0<$ x $<$ $.$

Form the general solution.