\[ -y'(x) \left (\frac {(2 v-1) g'(x)}{g(x)}+\frac {g''(x)}{g'(x)}+\frac {2 h'(x)}{h(x)}\right )+y(x) \left (g'(x)^2+\frac {h'(x) \left (\frac {(2 v-1) g'(x)}{g(x)}+\frac {g''(x)}{g'(x)}+\frac {2 h'(x)}{h(x)}\right )}{h(x)}-\frac {h''(x)}{h(x)}\right )+y''(x)=0 \] ✓ Mathematica : cpu = 0.158404 (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 = 0.094 (sec), leaf count = 24
\[\{y \left (x \right ) = \left (c_{1} \BesselJ \left (v , g \left (x \right )\right )+c_{2} \BesselY \left (v , g \left (x \right )\right )\right ) g \left (x \right )^{v} h \left (x \right )\}\]