\[ \boxed { \left ( {\frac { \left ( y \left ( x \right ) \right ) ^{2}}{b}}+{\frac {{x}^{2}}{a}} \right ) \left ( y \left ( x \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +x \right ) +{\frac { \left ( a-b \right ) \left ( y \left ( x \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -x \right ) }{a+b}}=0} \]
Mathematica: cpu = 0.245531 (sec), leaf count = 204 \[ \left \{\left \{y(x)\to -\frac {\sqrt {b} \sqrt {a^2+2 a^2 W\left (\frac {c_1 (a+b) e^{\frac {b x^2}{2 a^2}-\frac {b}{2 a}-\frac {x^2}{2 b}-\frac {1}{2}}}{2 a^3 b^2}\right )+a b-a x^2-b x^2}}{\sqrt {a} \sqrt {a+b}}\right \},\left \{y(x)\to \frac {\sqrt {b} \sqrt {a^2+2 a^2 W\left (\frac {c_1 (a+b) e^{\frac {b x^2}{2 a^2}-\frac {b}{2 a}-\frac {x^2}{2 b}-\frac {1}{2}}}{2 a^3 b^2}\right )+a b-a x^2-b x^2}}{\sqrt {a} \sqrt {a+b}}\right \}\right \} \]
Maple: cpu = 1.061 (sec), leaf count = 236 \[ \left \{ y \left ( x \right ) ={\frac {1}{a}\sqrt {a \left ( -b{x}^{2}+ab +{{\rm e}^{-{\frac {1}{2\,{a}^{2}b} \left ( 2\,{\it lambertW} \left ( 1/ 2\,{\frac { \left ( a+b \right ) {{\rm e}^{-1/2}}}{{a}^{2}b}{{\rm e}^{-1 /2\,{\frac {{x}^{2}}{b}}}}{{\rm e}^{1/2\,{\frac {b{x}^{2}}{{a}^{2}}}}} {{\rm e}^{-1/2\,{\frac {b}{a}}}} \left ( {{\rm e}^{{\frac {{\it \_C1}}{ ab}}}} \right ) ^{-1}} \right ) {a}^{2}b+{a}^{2}{x}^{2}-{b}^{2}{x}^{2}+{ a}^{2}b+a{b}^{2}+2\,{\it \_C1}\,a \right ) }}} \right ) }},y \left ( x \right ) =-{\frac {1}{a}\sqrt {a \left ( -b{x}^{2}+ab+{{\rm e}^{-{ \frac {1}{2\,{a}^{2}b} \left ( 2\,{\it lambertW} \left ( 1/2\,{\frac { \left ( a+b \right ) {{\rm e}^{-1/2}}}{{a}^{2}b}{{\rm e}^{-1/2\,{\frac {{x}^{2}}{b}}}}{{\rm e}^{1/2\,{\frac {b{x}^{2}}{{a}^{2}}}}}{{\rm e}^{- 1/2\,{\frac {b}{a}}}} \left ( {{\rm e}^{{\frac {{\it \_C1}}{ab}}}} \right ) ^{-1}} \right ) {a}^{2}b+{a}^{2}{x}^{2}-{b}^{2}{x}^{2}+{a}^{2} b+a{b}^{2}+2\,{\it \_C1}\,a \right ) }}} \right ) }} \right \} \]