\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) -y \left ( x \right ) h \left ( x,{\frac {{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }{y \left ( x \right ) }} \right ) =0} \]
Mathematica: cpu = 12.591099 (sec), leaf count = 26 \[ \text {DSolve}\left [y''(x)-y(x) h\left (x,\frac {y'(x)}{y(x)}\right )=0,y(x),x\right ] \]
Maple: cpu = 0.063 (sec), leaf count = 60 \[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {{\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}}},[ \left \{ {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) =- \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{2}+h \left ( {\it \_a},{\it \_b} \left ( {\it \_a} \right ) \right ) \right \} , \left \{ {\it \_a}=x,{\it \_b} \left ( {\it \_a} \right ) ={ \frac {{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }{y \left ( x \right ) }} \right \} , \left \{ x={\it \_a},y \left ( x \right ) ={ {\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+ {\it \_C1}}} \right \} ] \right ) \right \} \]