Repeated-root equation $y''-6y'+9y=0$ with boundary conditions

Solve \(y ^ { \prime \prime } - 6 y ^ { \prime } + 9 y = 0 { \mathrm { ~ w i t h ~ } } y ( 1 ) = 1 { \mathrm { ~ a n d ~ } } y ^ { \prime } ( 3 ) = 0\)