Question

Give the general solution to 2y"+72y+0 ; y_1=sin(6x)

Answer 1

I found that \[y_{2}\]=u"sin(6x)+12u'cos(6x)-36usin(6x)

Answer 2

\[\large 2y''+72y\color{red}{=}0\]Was this a typo? The part in red.
Hmm I'm not quite sure how you're approaching this. I'm a little confused by the u's.

Answer 3

yes sorry

Answer 4

its the reduction of order method

Answer 5

i.e.