\[ \text {Global$\grave { }$a} \text {Global$\grave { }$x} \text {Global$\grave { }$y}'(\text {Global$\grave { }$x})-\text {Global$\grave { }$b} \text {Global$\grave { }$x}^2-\text {Global$\grave { }$c}+\text {Global$\grave { }$y}'(\text {Global$\grave { }$x})^2=0 \] ✓ Mathematica : cpu = 0.25367 (sec), leaf count = 201
\[\left \{\left \{\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\to c_1+\frac {1}{2} \left (\frac {1}{2} \text {Global$\grave { }$x} \sqrt {\text {Global$\grave { }$a}^2 \text {Global$\grave { }$x}^2+4 \text {Global$\grave { }$b} \text {Global$\grave { }$x}^2+4 \text {Global$\grave { }$c}}+\frac {2 \text {Global$\grave { }$c} \log \left (\sqrt {\text {Global$\grave { }$a}^2+4 \text {Global$\grave { }$b}} \sqrt {\text {Global$\grave { }$a}^2 \text {Global$\grave { }$x}^2+4 \text {Global$\grave { }$b} \text {Global$\grave { }$x}^2+4 \text {Global$\grave { }$c}}+\text {Global$\grave { }$a}^2 \text {Global$\grave { }$x}+4 \text {Global$\grave { }$b} \text {Global$\grave { }$x}\right )}{\sqrt {\text {Global$\grave { }$a}^2+4 \text {Global$\grave { }$b}}}-\frac {\text {Global$\grave { }$a} \text {Global$\grave { }$x}^2}{2}\right )\right \},\left \{\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\to c_1+\frac {1}{2} \left (-\frac {1}{2} \text {Global$\grave { }$x} \left (\sqrt {\text {Global$\grave { }$x}^2 \left (\text {Global$\grave { }$a}^2+4 \text {Global$\grave { }$b}\right )+4 \text {Global$\grave { }$c}}+\text {Global$\grave { }$a} \text {Global$\grave { }$x}\right )-\frac {2 \text {Global$\grave { }$c} \log \left (\sqrt {\text {Global$\grave { }$a}^2+4 \text {Global$\grave { }$b}} \sqrt {\text {Global$\grave { }$x}^2 \left (\text {Global$\grave { }$a}^2+4 \text {Global$\grave { }$b}\right )+4 \text {Global$\grave { }$c}}+\text {Global$\grave { }$a}^2 \text {Global$\grave { }$x}+4 \text {Global$\grave { }$b} \text {Global$\grave { }$x}\right )}{\sqrt {\text {Global$\grave { }$a}^2+4 \text {Global$\grave { }$b}}}\right )\right \}\right \}\]
✓ Maple : cpu = 0.655 (sec), leaf count = 146
\[ \left \{ y \left ( x \right ) =-{\frac {a{x}^{2}}{4}}-{\frac {x}{4}\sqrt { \left ( {a}^{2}+4\,b \right ) {x}^{2}+4\,c}}-{c\ln \left ( \sqrt {{a}^{2}+4\,b}x+\sqrt { \left ( {a}^{2}+4\,b \right ) {x}^{2}+4\,c} \right ) {\frac {1}{\sqrt {{a}^{2}+4\,b}}}}+{\it \_C1},y \left ( x \right ) =-{\frac {a{x}^{2}}{4}}+{\frac {x}{4}\sqrt { \left ( {a}^{2}+4\,b \right ) {x}^{2}+4\,c}}+{c\ln \left ( \sqrt {{a}^{2}+4\,b}x+\sqrt { \left ( {a}^{2}+4\,b \right ) {x}^{2}+4\,c} \right ) {\frac {1}{\sqrt {{a}^{2}+4\,b}}}}+{\it \_C1} \right \} \]