\[ -4 a^2 y(x)-3 a y(x)^2-b+y''(x)-3 y(x) y'(x)=0 \] ✓ Mathematica : cpu = 11.5533 (sec), leaf count = 1670
\[\left \{\left \{y(x)\to \frac {\sqrt {b} \sqrt {\frac {e^{-2 a x}}{b}} \sqrt {c_1} \left (-i^{\frac {\sqrt {4 a^3-3 b}}{a^{3/2}}} 2^{\frac {3 \sqrt {4 a^6-3 a^3 b}}{2 a^3}+\frac {1}{2}} 3^{\frac {1}{2} \left (\frac {\sqrt {4 a^3-3 b}}{a^{3/2}}-1\right )} a^{\frac {\sqrt {4 a^6-3 a^3 b}}{a^3}} b^{\frac {1}{2} \left (\frac {\sqrt {4 a^3-3 b}}{a^{3/2}}-1\right )} \left (2 a^3-\sqrt {4 a^3-3 b} a^{3/2}+\sqrt {4 a^6-3 a^3 b}\right ) \left (\frac {e^{-2 a x}}{b}\right )^{\frac {1}{2} \left (\frac {\sqrt {4 a^3-3 b}}{a^{3/2}}-1\right )} I_{\frac {\sqrt {4 a^6-3 a^3 b}}{2 a^3}}\left (\frac {\sqrt {\frac {3}{2}} \sqrt {b} \sqrt {\frac {e^{-2 a x}}{b}} \sqrt {c_1}}{a}\right ) \Gamma \left (\frac {\sqrt {4 a^6-3 a^3 b}}{2 a^3}+1\right ) c_1^{\frac {1}{2} \left (\frac {\sqrt {4 a^3-3 b}}{a^{3/2}}-1\right )}+i^{\frac {\sqrt {4 a^3-3 b}}{a^{3/2}}} 2^{\frac {3 \sqrt {4 a^6-3 a^3 b}}{2 a^3}} 3^{\frac {\sqrt {4 a^3-3 b}}{2 a^{3/2}}} a^{\frac {\sqrt {4 a^6-3 a^3 b}}{a^3}+2} b^{\frac {\sqrt {4 a^3-3 b}}{2 a^{3/2}}} \left (\frac {e^{-2 a x}}{b}\right )^{\frac {\sqrt {4 a^3-3 b}}{2 a^{3/2}}} \left (I_{\frac {\sqrt {4 a^6-3 a^3 b}}{2 a^3}-1}\left (\frac {\sqrt {\frac {3}{2}} \sqrt {b} \sqrt {\frac {e^{-2 a x}}{b}} \sqrt {c_1}}{a}\right )+I_{\frac {\sqrt {4 a^6-3 a^3 b}}{2 a^3}+1}\left (\frac {\sqrt {\frac {3}{2}} \sqrt {b} \sqrt {\frac {e^{-2 a x}}{b}} \sqrt {c_1}}{a}\right )\right ) \Gamma \left (\frac {\sqrt {4 a^6-3 a^3 b}}{2 a^3}+1\right ) c_1^{\frac {\sqrt {4 a^3-3 b}}{2 a^{3/2}}}+2^{\frac {3 \sqrt {4 a^3-3 b}}{2 a^{3/2}}} 3^{\frac {\sqrt {4 a^6-3 a^3 b}}{2 a^3}-\frac {1}{2}} a^{\frac {\sqrt {4 a^3-3 b}}{a^{3/2}}} b^{\frac {\sqrt {4 a^6-3 a^3 b}}{2 a^3}-\frac {1}{2}} \left (\frac {e^{-2 a x}}{b}\right )^{\frac {\sqrt {4 a^6-3 a^3 b}}{2 a^3}-\frac {1}{2}} \left (\sqrt {3} \sqrt {b} \sqrt {\frac {e^{-2 a x}}{b}} \left (I_{-\frac {\sqrt {4 a^6-3 a^3 b}}{2 a^3}-1}\left (\frac {\sqrt {\frac {3}{2}} \sqrt {b} \sqrt {\frac {e^{-2 a x}}{b}} \sqrt {c_1}}{a}\right )+I_{1-\frac {\sqrt {4 a^6-3 a^3 b}}{2 a^3}}\left (\frac {\sqrt {\frac {3}{2}} \sqrt {b} \sqrt {\frac {e^{-2 a x}}{b}} \sqrt {c_1}}{a}\right )\right ) \sqrt {c_1} a^2+\sqrt {2} \left (-2 a^3-\sqrt {4 a^3-3 b} a^{3/2}+\sqrt {4 a^6-3 a^3 b}\right ) I_{-\frac {\sqrt {4 a^6-3 a^3 b}}{2 a^3}}\left (\frac {\sqrt {\frac {3}{2}} \sqrt {b} \sqrt {\frac {e^{-2 a x}}{b}} \sqrt {c_1}}{a}\right )\right ) c_2 \Gamma \left (1-\frac {\sqrt {4 a^6-3 a^3 b}}{2 a^3}\right ) c_1^{\frac {\sqrt {4 a^6-3 a^3 b}}{2 a^3}-\frac {1}{2}}\right )}{\sqrt {6} a^2 \left (i^{\frac {\sqrt {4 a^3-3 b}}{a^{3/2}}} 2^{\frac {3 \sqrt {4 a^6-3 a^3 b}}{2 a^3}} 3^{\frac {\sqrt {4 a^3-3 b}}{2 a^{3/2}}} a^{\frac {\sqrt {4 a^6-3 a^3 b}}{a^3}} b^{\frac {\sqrt {4 a^3-3 b}}{2 a^{3/2}}} \left (\frac {e^{-2 a x}}{b}\right )^{\frac {\sqrt {4 a^3-3 b}}{2 a^{3/2}}} I_{\frac {\sqrt {4 a^6-3 a^3 b}}{2 a^3}}\left (\frac {\sqrt {\frac {3}{2}} \sqrt {b} \sqrt {\frac {e^{-2 a x}}{b}} \sqrt {c_1}}{a}\right ) \Gamma \left (\frac {\sqrt {4 a^6-3 a^3 b}}{2 a^3}+1\right ) c_1^{\frac {\sqrt {4 a^3-3 b}}{2 a^{3/2}}}+2^{\frac {3 \sqrt {4 a^3-3 b}}{2 a^{3/2}}} 3^{\frac {\sqrt {4 a^6-3 a^3 b}}{2 a^3}} a^{\frac {\sqrt {4 a^3-3 b}}{a^{3/2}}} b^{\frac {\sqrt {4 a^6-3 a^3 b}}{2 a^3}} \left (\frac {e^{-2 a x}}{b}\right )^{\frac {\sqrt {4 a^6-3 a^3 b}}{2 a^3}} I_{-\frac {\sqrt {4 a^6-3 a^3 b}}{2 a^3}}\left (\frac {\sqrt {\frac {3}{2}} \sqrt {b} \sqrt {\frac {e^{-2 a x}}{b}} \sqrt {c_1}}{a}\right ) c_2 \Gamma \left (1-\frac {\sqrt {4 a^6-3 a^3 b}}{2 a^3}\right ) c_1^{\frac {\sqrt {4 a^6-3 a^3 b}}{2 a^3}}\right )}\right \}\right \}\]
✓ Maple : cpu = 0.702 (sec), leaf count = 783
\[ \left \{ \int ^{y \left ( x \right ) }\!-6\,{{a}^{2} \left ( -12\,{\it \_a}\,{a}^{3}-9\,{{\it \_a}}^{2}{a}^{2}+ \left ( {\it RootOf} \left ( 2\,{{\sl K}_{1/2\,{\frac {4\,{a}^{3}-3\,b}{\sqrt {4\,{a}^{4}-3\,ab}a}}}\left (-1/2\,{\frac {{\it \_Z}}{{a}^{2}}}\right )}{\it \_C1}\,{a}^{2}+3\,{{\sl K}_{1/2\,{\frac {4\,{a}^{3}-3\,b}{\sqrt {4\,{a}^{4}-3\,ab}a}}}\left (-1/2\,{\frac {{\it \_Z}}{{a}^{2}}}\right )}{\it \_C1}\,a{\it \_a}+\sqrt {4\,{a}^{4}-3\,ab}{{\sl K}_{1/2\,{\frac {4\,{a}^{3}-3\,b}{\sqrt {4\,{a}^{4}-3\,ab}a}}}\left (-1/2\,{\frac {{\it \_Z}}{{a}^{2}}}\right )}{\it \_C1}+2\,{{\sl I}_{-1/2\,{\frac {4\,{a}^{3}-3\,b}{\sqrt {4\,{a}^{4}-3\,ab}a}}}\left (-1/2\,{\frac {{\it \_Z}}{{a}^{2}}}\right )}{a}^{2}+3\,{{\sl I}_{-1/2\,{\frac {4\,{a}^{3}-3\,b}{\sqrt {4\,{a}^{4}-3\,ab}a}}}\left (-1/2\,{\frac {{\it \_Z}}{{a}^{2}}}\right )}a{\it \_a}+{\it \_Z}\,{{\sl K}_{1/2\,{\frac {-4\,{a}^{3}+2\,\sqrt {4\,{a}^{4}-3\,ab}a+3\,b}{\sqrt {4\,{a}^{4}-3\,ab}a}}}\left (-1/2\,{\frac {{\it \_Z}}{{a}^{2}}}\right )}{\it \_C1}+\sqrt {4\,{a}^{4}-3\,ab}{{\sl I}_{-1/2\,{\frac {4\,{a}^{3}-3\,b}{\sqrt {4\,{a}^{4}-3\,ab}a}}}\left (-1/2\,{\frac {{\it \_Z}}{{a}^{2}}}\right )}-{\it \_Z}\,{{\sl I}_{1/2\,{\frac {-4\,{a}^{3}+2\,\sqrt {4\,{a}^{4}-3\,ab}a+3\,b}{\sqrt {4\,{a}^{4}-3\,ab}a}}}\left (-1/2\,{\frac {{\it \_Z}}{{a}^{2}}}\right )} \right ) \right ) ^{2}-3\,ab \right ) ^{-1}}{d{\it \_a}}-x-{\it \_C2}=0,\int ^{y \left ( x \right ) }\!-6\,{{a}^{2} \left ( -12\,{\it \_a}\,{a}^{3}-9\,{{\it \_a}}^{2}{a}^{2}+ \left ( {\it RootOf} \left ( 2\,{{\sl K}_{1/2\,{\frac {4\,{a}^{3}-3\,b}{\sqrt {4\,{a}^{4}-3\,ab}a}}}\left (1/2\,{\frac {{\it \_Z}}{{a}^{2}}}\right )}{\it \_C1}\,{a}^{2}+3\,{{\sl K}_{1/2\,{\frac {4\,{a}^{3}-3\,b}{\sqrt {4\,{a}^{4}-3\,ab}a}}}\left (1/2\,{\frac {{\it \_Z}}{{a}^{2}}}\right )}{\it \_C1}\,a{\it \_a}+\sqrt {4\,{a}^{4}-3\,ab}{{\sl K}_{1/2\,{\frac {4\,{a}^{3}-3\,b}{\sqrt {4\,{a}^{4}-3\,ab}a}}}\left (1/2\,{\frac {{\it \_Z}}{{a}^{2}}}\right )}{\it \_C1}+2\,{{\sl I}_{-1/2\,{\frac {4\,{a}^{3}-3\,b}{\sqrt {4\,{a}^{4}-3\,ab}a}}}\left (1/2\,{\frac {{\it \_Z}}{{a}^{2}}}\right )}{a}^{2}+3\,{{\sl I}_{-1/2\,{\frac {4\,{a}^{3}-3\,b}{\sqrt {4\,{a}^{4}-3\,ab}a}}}\left (1/2\,{\frac {{\it \_Z}}{{a}^{2}}}\right )}a{\it \_a}+{\it \_Z}\,{{\sl K}_{1/2\,{\frac {-4\,{a}^{3}+2\,\sqrt {4\,{a}^{4}-3\,ab}a+3\,b}{\sqrt {4\,{a}^{4}-3\,ab}a}}}\left (1/2\,{\frac {{\it \_Z}}{{a}^{2}}}\right )}{\it \_C1}+\sqrt {4\,{a}^{4}-3\,ab}{{\sl I}_{-1/2\,{\frac {4\,{a}^{3}-3\,b}{\sqrt {4\,{a}^{4}-3\,ab}a}}}\left (1/2\,{\frac {{\it \_Z}}{{a}^{2}}}\right )}-{\it \_Z}\,{{\sl I}_{1/2\,{\frac {-4\,{a}^{3}+2\,\sqrt {4\,{a}^{4}-3\,ab}a+3\,b}{\sqrt {4\,{a}^{4}-3\,ab}a}}}\left (1/2\,{\frac {{\it \_Z}}{{a}^{2}}}\right )} \right ) \right ) ^{2}-3\,ab \right ) ^{-1}}{d{\it \_a}}-x-{\it \_C2}=0 \right \} \]