$a$ is a constant and the solution passes through the points $(2,1)$ and $(4,4)$
Here are the steps I used to get my answer:
$ty' - ay = 0$
$y' - (a/t)y = 0$
$p(t) = -a/t$, $P(t) = -aln|t|$
$μ(t) = e^{P(t)} = e^{-aln|t|}$
$y'e^{-aln|t|} - (a/t)ye^{-aln|t|} = 0$
$(ye^{-aln|t|})' = 0$
$ye^{-aln|t|} = C$
$y = Ce^{aln|t|}$
Plugging in my two points, I get:
$1 = Ce^{aln|2|}$
$4 = Ce^{aln|4|}$
Dividing these two equations, I get:
$4 = e^{aln(2)}$
$ln(4) = aln(2)$
$a = ln(2)$
But the answer to my book says $a = 2$, and I can't seem to find my mistake.