\[ -y'(x) \left (\frac {(2 v-1) g'(x)}{g(x)}+\frac {g''(x)}{g'(x)}+\frac {2 h'(x)}{h(x)}\right )+y(x) \left (\frac {h'(x) \left (\frac {(2 v-1) g'(x)}{g(x)}+\frac {g''(x)}{g'(x)}+\frac {2 h'(x)}{h(x)}\right )}{h(x)}+g'(x)^2-\frac {h''(x)}{h(x)}\right )+y''(x)=0 \] ✓ Mathematica : cpu = 0.153514 (sec), leaf count = 32
\[\left \{\left \{y(x)\to c_1 h(x) g(x)^v J_v(g(x))+c_2 h(x) g(x)^v Y_v(g(x))\right \}\right \}\] ✓ Maple : cpu = 0.195 (sec), leaf count = 24
\[ \left \{ y \left ( x \right ) =h \left ( x \right ) \left ( g \left ( x \right ) \right ) ^{v} \left ( {{\sl Y}_{v}\left (g \left ( x \right ) \right )}{\it \_C2}+{{\sl J}_{v}\left (g \left ( x \right ) \right )}{\it \_C1} \right ) \right \} \]