$v = y^{1/2}, v' + \frac{1}{2}v = \frac{1}{2}x$

$v = y^{1/2}, v' + v = x$

$v = y^{-1/2}, v' - \frac{1}{2}v = -\frac{1}{2}x$

$v = y^{3/2}, v' + \frac{3}{2}v = \frac{3}{2}x$