\[ \left (\text {Global$\grave { }$y}(\text {Global$\grave { }$x}) \text {Global$\grave { }$y}'(\text {Global$\grave { }$x})+\text {Global$\grave { }$x}\right ) \left (\frac {\text {Global$\grave { }$x}^2}{\text {Global$\grave { }$a}}+\frac {\text {Global$\grave { }$y}(\text {Global$\grave { }$x})^2}{\text {Global$\grave { }$b}}\right )+\frac {(\text {Global$\grave { }$a}-\text {Global$\grave { }$b}) \left (\text {Global$\grave { }$y}(\text {Global$\grave { }$x}) \text {Global$\grave { }$y}'(\text {Global$\grave { }$x})-\text {Global$\grave { }$x}\right )}{\text {Global$\grave { }$a}+\text {Global$\grave { }$b}}=0 \] ✓ Mathematica : cpu = 0.271793 (sec), leaf count = 204
\[\left \{\left \{\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\to -\frac {\sqrt {\text {Global$\grave { }$b}} \sqrt {2 \text {Global$\grave { }$a}^2 W\left (\frac {c_1 (\text {Global$\grave { }$a}+\text {Global$\grave { }$b}) e^{\frac {\text {Global$\grave { }$b} \text {Global$\grave { }$x}^2}{2 \text {Global$\grave { }$a}^2}-\frac {\text {Global$\grave { }$b}}{2 \text {Global$\grave { }$a}}-\frac {\text {Global$\grave { }$x}^2}{2 \text {Global$\grave { }$b}}-\frac {1}{2}}}{2 \text {Global$\grave { }$a}^3 \text {Global$\grave { }$b}^2}\right )+\text {Global$\grave { }$a}^2+\text {Global$\grave { }$a} \text {Global$\grave { }$b}-\text {Global$\grave { }$a} \text {Global$\grave { }$x}^2-\text {Global$\grave { }$b} \text {Global$\grave { }$x}^2}}{\sqrt {\text {Global$\grave { }$a}} \sqrt {\text {Global$\grave { }$a}+\text {Global$\grave { }$b}}}\right \},\left \{\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\to \frac {\sqrt {\text {Global$\grave { }$b}} \sqrt {2 \text {Global$\grave { }$a}^2 W\left (\frac {c_1 (\text {Global$\grave { }$a}+\text {Global$\grave { }$b}) e^{\frac {\text {Global$\grave { }$b} \text {Global$\grave { }$x}^2}{2 \text {Global$\grave { }$a}^2}-\frac {\text {Global$\grave { }$b}}{2 \text {Global$\grave { }$a}}-\frac {\text {Global$\grave { }$x}^2}{2 \text {Global$\grave { }$b}}-\frac {1}{2}}}{2 \text {Global$\grave { }$a}^3 \text {Global$\grave { }$b}^2}\right )+\text {Global$\grave { }$a}^2+\text {Global$\grave { }$a} \text {Global$\grave { }$b}-\text {Global$\grave { }$a} \text {Global$\grave { }$x}^2-\text {Global$\grave { }$b} \text {Global$\grave { }$x}^2}}{\sqrt {\text {Global$\grave { }$a}} \sqrt {\text {Global$\grave { }$a}+\text {Global$\grave { }$b}}}\right \}\right \}\]
✓ Maple : cpu = 1.631 (sec), leaf count = 236
\[ \left \{ y \left ( x \right ) ={\frac {1}{a}\sqrt {a \left ( -b{x}^{2}+ab+{{\rm e}^{-{\frac {1}{2\,b{a}^{2}} \left ( 2\,{\it lambertW} \left ( 1/2\,{\frac { \left ( a+b \right ) {{\rm e}^{-1/2}}}{b{a}^{2}}{{\rm e}^{-1/2\,{\frac {{x}^{2}}{b}}}}{{\rm e}^{1/2\,{\frac {b{x}^{2}}{{a}^{2}}}}}{{\rm e}^{-1/2\,{\frac {b}{a}}}} \left ( {{\rm e}^{{\frac {{\it \_C1}}{ab}}}} \right ) ^{-1}} \right ) b{a}^{2}+{a}^{2}{x}^{2}-{b}^{2}{x}^{2}+b{a}^{2}+a{b}^{2}+2\,{\it \_C1}\,a \right ) }}} \right ) }},y \left ( x \right ) =-{\frac {1}{a}\sqrt {a \left ( -b{x}^{2}+ab+{{\rm e}^{-{\frac {1}{2\,b{a}^{2}} \left ( 2\,{\it lambertW} \left ( 1/2\,{\frac { \left ( a+b \right ) {{\rm e}^{-1/2}}}{b{a}^{2}}{{\rm e}^{-1/2\,{\frac {{x}^{2}}{b}}}}{{\rm e}^{1/2\,{\frac {b{x}^{2}}{{a}^{2}}}}}{{\rm e}^{-1/2\,{\frac {b}{a}}}} \left ( {{\rm e}^{{\frac {{\it \_C1}}{ab}}}} \right ) ^{-1}} \right ) b{a}^{2}+{a}^{2}{x}^{2}-{b}^{2}{x}^{2}+b{a}^{2}+a{b}^{2}+2\,{\it \_C1}\,a \right ) }}} \right ) }} \right \} \]