\[ -\left (\text {Global$\grave { }$g}(\text {Global$\grave { }$x})-\text {Global$\grave { }$f}(\text {Global$\grave { }$x})^2\right ) e^{-2 \int _{\text {Global$\grave { }$a}}^{\text {Global$\grave { }$x}} \text {Global$\grave { }$f}(\text {Global$\grave { }$xp}) \, d\text {Global$\grave { }$xp}}+2 \text {Global$\grave { }$f}(\text {Global$\grave { }$x}) \text {Global$\grave { }$y}(\text {Global$\grave { }$x}) \text {Global$\grave { }$y}'(\text {Global$\grave { }$x})+\text {Global$\grave { }$g}(\text {Global$\grave { }$x}) \text {Global$\grave { }$y}(\text {Global$\grave { }$x})^2+\text {Global$\grave { }$y}'(\text {Global$\grave { }$x})^2=0 \] ✗ Mathematica : cpu = 53.3292 (sec), leaf count = 0 , could not solve
DSolve[-((-Global`f[Global`x]^2 + Global`g[Global`x])/E^(2*Integrate[Global`f[Global`xp], {Global`xp, Global`a, Global`x}])) + Global`g[Global`x]*Global`y[Global`x]^2 + 2*Global`f[Global`x]*Global`y[Global`x]*Derivative[1][Global`y][Global`x] + Derivative[1][Global`y][Global`x]^2 == 0, Global`y[Global`x], Global`x]
✓ Maple : cpu = 5.172 (sec), leaf count = 307
\[ \left \{ y \left ( x \right ) =\tan \left ( {\frac {1}{2\,\cos \left ( 2 \right ) +2} \left ( 2\,{\it \_C1}\,\cos \left ( 2 \right ) +2\,{\it \_C1}-\int \! \left ( {{\rm e}^{\int _{a}^{x}\!f \left ( {\it xp} \right ) \,{\rm d}{\it xp}}} \right ) ^{2}\sqrt {-2\,{\frac { \left ( f \left ( x \right ) \right ) ^{2}\cos \left ( 4 \right ) }{ \left ( {{\rm e}^{\int _{a}^{x}\!f \left ( {\it xp} \right ) \,{\rm d}{\it xp}}} \right ) ^{4}}}-8\,{\frac { \left ( f \left ( x \right ) \right ) ^{2}\cos \left ( 2 \right ) }{ \left ( {{\rm e}^{\int _{a}^{x}\!f \left ( {\it xp} \right ) \,{\rm d}{\it xp}}} \right ) ^{4}}}-6\,{\frac { \left ( f \left ( x \right ) \right ) ^{2}}{ \left ( {{\rm e}^{\int _{a}^{x}\!f \left ( {\it xp} \right ) \,{\rm d}{\it xp}}} \right ) ^{4}}}+2\,{\frac {g \left ( x \right ) \cos \left ( 4 \right ) }{ \left ( {{\rm e}^{\int _{a}^{x}\!f \left ( {\it xp} \right ) \,{\rm d}{\it xp}}} \right ) ^{4}}}+8\,{\frac {g \left ( x \right ) \cos \left ( 2 \right ) }{ \left ( {{\rm e}^{\int _{a}^{x}\!f \left ( {\it xp} \right ) \,{\rm d}{\it xp}}} \right ) ^{4}}}+6\,{\frac {g \left ( x \right ) }{ \left ( {{\rm e}^{\int _{a}^{x}\!f \left ( {\it xp} \right ) \,{\rm d}{\it xp}}} \right ) ^{4}}}}\,{\rm d}x \right ) } \right ) \sqrt {{{{\rm e}^{-2\,\int _{a}^{x}\!f \left ( {\it xp} \right ) \,{\rm d}{\it xp}}} \left ( \left ( \tan \left ( {\frac {1}{2\,\cos \left ( 2 \right ) +2} \left ( 2\,{\it \_C1}\,\cos \left ( 2 \right ) +2\,{\it \_C1}-\int \! \left ( {{\rm e}^{\int _{a}^{x}\!f \left ( {\it xp} \right ) \,{\rm d}{\it xp}}} \right ) ^{2}\sqrt {-2\,{\frac { \left ( f \left ( x \right ) \right ) ^{2}\cos \left ( 4 \right ) }{ \left ( {{\rm e}^{\int _{a}^{x}\!f \left ( {\it xp} \right ) \,{\rm d}{\it xp}}} \right ) ^{4}}}-8\,{\frac { \left ( f \left ( x \right ) \right ) ^{2}\cos \left ( 2 \right ) }{ \left ( {{\rm e}^{\int _{a}^{x}\!f \left ( {\it xp} \right ) \,{\rm d}{\it xp}}} \right ) ^{4}}}-6\,{\frac { \left ( f \left ( x \right ) \right ) ^{2}}{ \left ( {{\rm e}^{\int _{a}^{x}\!f \left ( {\it xp} \right ) \,{\rm d}{\it xp}}} \right ) ^{4}}}+2\,{\frac {g \left ( x \right ) \cos \left ( 4 \right ) }{ \left ( {{\rm e}^{\int _{a}^{x}\!f \left ( {\it xp} \right ) \,{\rm d}{\it xp}}} \right ) ^{4}}}+8\,{\frac {g \left ( x \right ) \cos \left ( 2 \right ) }{ \left ( {{\rm e}^{\int _{a}^{x}\!f \left ( {\it xp} \right ) \,{\rm d}{\it xp}}} \right ) ^{4}}}+6\,{\frac {g \left ( x \right ) }{ \left ( {{\rm e}^{\int _{a}^{x}\!f \left ( {\it xp} \right ) \,{\rm d}{\it xp}}} \right ) ^{4}}}}\,{\rm d}x \right ) } \right ) \right ) ^{2}+1 \right ) ^{-1}}} \right \} \]