Question

power series solution y' + y/x = 0

Answer 1

xy'+y=0
(xy)'=0
xy=C
y=C/x

Answer 2

\[dy/dx + y/x = 0\]
\[dy/dx = -y/x\]
\[dy/y = -dx/x\]
\[\int\limits(dy/y) = \int\limits(-dx/x)\]
\[lny = -lnx + lnk\]
\[lny = -\ln(x/k)\]
\[e ^{lny} = e^{-\ln(x/k)}\]
\[y = k/x\], where k is an arbitrary constant.