\[ \text {Global$\grave { }$a} \text {Global$\grave { }$y}(\text {Global$\grave { }$x}) \text {Global$\grave { }$y}'(\text {Global$\grave { }$x})-\text {Global$\grave { }$b} \text {Global$\grave { }$x}-\text {Global$\grave { }$c}+\text {Global$\grave { }$y}'(\text {Global$\grave { }$x})^2=0 \] ✓ Mathematica : cpu = 2.07002 (sec), leaf count = 142
\[\text {Solve}\left [\left \{\text {Global$\grave { }$x}=c_1 e^{\text {Global$\grave { }$b} \left (\frac {\log (\text {K$\$$954422})}{\text {Global$\grave { }$b}}-\frac {\log \left (\text {Global$\grave { }$b}-\text {Global$\grave { }$a} \text {K$\$$954422}^2\right )}{2 \text {Global$\grave { }$b}}\right )}+e^{\text {Global$\grave { }$b} \left (\frac {\log (\text {K$\$$954422})}{\text {Global$\grave { }$b}}-\frac {\log \left (\text {Global$\grave { }$b}-\text {Global$\grave { }$a} \text {K$\$$954422}^2\right )}{2 \text {Global$\grave { }$b}}\right )} \left (\frac {\tan ^{-1}\left (\frac {\sqrt {\text {Global$\grave { }$a}} \text {K$\$$954422}}{\sqrt {\text {Global$\grave { }$b}-\text {Global$\grave { }$a} \text {K$\$$954422}^2}}\right )}{\sqrt {\text {Global$\grave { }$a}}}-\frac {\text {Global$\grave { }$c} \sqrt {\text {Global$\grave { }$b}-\text {Global$\grave { }$a} \text {K$\$$954422}^2}}{\text {Global$\grave { }$b} \text {K$\$$954422}}\right ),\text {Global$\grave { }$y}(\text {Global$\grave { }$x})=\frac {\text {Global$\grave { }$b} \text {Global$\grave { }$x}}{\text {Global$\grave { }$a} \text {K$\$$954422}}+\frac {\text {Global$\grave { }$c}-\text {K$\$$954422}^2}{\text {Global$\grave { }$a} \text {K$\$$954422}}\right \},\{\text {Global$\grave { }$y}(\text {Global$\grave { }$x}),\text {K$\$$954422}\}\right ]\]
✓ Maple : cpu = 0.257 (sec), leaf count = 416
\[ \left \{ y \left ( x \right ) =2\,{\frac {b{{\rm e}^{{\it RootOf} \left ( \sqrt {a}{\it \_C1}\,b{{\rm e}^{2\,{\it \_Z}}}-a{{\rm e}^{2\,{\it \_Z}}}bx+\sqrt {a}{\it \_C1}\,{b}^{2}-{{\rm e}^{2\,{\it \_Z}}}{\it \_Z}\,b-a{{\rm e}^{2\,{\it \_Z}}}c+a{b}^{2}x-{b}^{2}{\it \_Z}+abc \right ) }}x}{ \left ( {{\rm e}^{2\,{\it RootOf} \left ( \sqrt {a}{\it \_C1}\,b{{\rm e}^{2\,{\it \_Z}}}-a{{\rm e}^{2\,{\it \_Z}}}bx+\sqrt {a}{\it \_C1}\,{b}^{2}-{{\rm e}^{2\,{\it \_Z}}}{\it \_Z}\,b-a{{\rm e}^{2\,{\it \_Z}}}c+a{b}^{2}x-{b}^{2}{\it \_Z}+abc \right ) }}+b \right ) \sqrt {a}}}+2\,{\frac {{{\rm e}^{{\it RootOf} \left ( \sqrt {a}{\it \_C1}\,b{{\rm e}^{2\,{\it \_Z}}}-a{{\rm e}^{2\,{\it \_Z}}}bx+\sqrt {a}{\it \_C1}\,{b}^{2}-{{\rm e}^{2\,{\it \_Z}}}{\it \_Z}\,b-a{{\rm e}^{2\,{\it \_Z}}}c+a{b}^{2}x-{b}^{2}{\it \_Z}+abc \right ) }}}{ \left ( {{\rm e}^{2\,{\it RootOf} \left ( \sqrt {a}{\it \_C1}\,b{{\rm e}^{2\,{\it \_Z}}}-a{{\rm e}^{2\,{\it \_Z}}}bx+\sqrt {a}{\it \_C1}\,{b}^{2}-{{\rm e}^{2\,{\it \_Z}}}{\it \_Z}\,b-a{{\rm e}^{2\,{\it \_Z}}}c+a{b}^{2}x-{b}^{2}{\it \_Z}+abc \right ) }}+b \right ) \sqrt {a}} \left ( -1/4\,{\frac { \left ( {{\rm e}^{2\,{\it RootOf} \left ( \sqrt {a}{\it \_C1}\,b{{\rm e}^{2\,{\it \_Z}}}-a{{\rm e}^{2\,{\it \_Z}}}bx+\sqrt {a}{\it \_C1}\,{b}^{2}-{{\rm e}^{2\,{\it \_Z}}}{\it \_Z}\,b-a{{\rm e}^{2\,{\it \_Z}}}c+a{b}^{2}x-{b}^{2}{\it \_Z}+abc \right ) }}+b \right ) ^{2}{{\rm e}^{-2\,{\it RootOf} \left ( \sqrt {a}{\it \_C1}\,b{{\rm e}^{2\,{\it \_Z}}}-a{{\rm e}^{2\,{\it \_Z}}}bx+\sqrt {a}{\it \_C1}\,{b}^{2}-{{\rm e}^{2\,{\it \_Z}}}{\it \_Z}\,b-a{{\rm e}^{2\,{\it \_Z}}}c+a{b}^{2}x-{b}^{2}{\it \_Z}+abc \right ) }}}{a}}+c \right ) } \right \} \]