\[ 2 a^2 y(x)^2-(a y(x)-1) y'(x)+a y(x)-2 b^2 y(x)^3+y(x) y''(x)-y'(x)^2=0 \] ✓ Mathematica : cpu = 52.4583 (sec), leaf count = 543
\[\left \{\left \{y(x)\to -\frac {1}{2 a}+e^{2 a x} \left (\frac {e^{-2 a x} \left (c_1 \left (\sqrt {a^3+2 b^2}-a^{3/2}\right ) \Gamma \left (1-\frac {\sqrt {a^3+2 b^2}}{2 a^{3/2}}\right ) J_{-\frac {\sqrt {a^3+2 b^2}}{2 a^{3/2}}}\left (\frac {\sqrt {a b^2 e^{2 a x} c_2}}{a^{3/2}}\right )+2 c_1 \Gamma \left (1-\frac {\sqrt {a^3+2 b^2}}{2 a^{3/2}}\right ) \sqrt {a b^2 c_2 e^{2 a x}} J_{1-\frac {\sqrt {a^3+2 b^2}}{2 a^{3/2}}}\left (\frac {\sqrt {a b^2 e^{2 a x} c_2}}{a^{3/2}}\right )+\Gamma \left (\frac {\sqrt {a^3+2 b^2}}{2 a^{3/2}}+1\right ) \left (\left (-a^{3/2}-\sqrt {a^3+2 b^2}\right ) J_{\frac {\sqrt {a^3+2 b^2}}{2 a^{3/2}}}\left (\frac {\sqrt {a b^2 e^{2 a x} c_2}}{a^{3/2}}\right )+2 \sqrt {a b^2 c_2 e^{2 a x}} J_{\frac {\sqrt {a^3+2 b^2}}{2 a^{3/2}}+1}\left (\frac {\sqrt {a b^2 e^{2 a x} c_2}}{a^{3/2}}\right )\right )\right ){}^2}{4 a \left (b c_1 \Gamma \left (1-\frac {\sqrt {a^3+2 b^2}}{2 a^{3/2}}\right ) J_{-\frac {\sqrt {a^3+2 b^2}}{2 a^{3/2}}}\left (\frac {\sqrt {a b^2 e^{2 a x} c_2}}{a^{3/2}}\right )+b \Gamma \left (\frac {\sqrt {a^3+2 b^2}}{2 a^{3/2}}+1\right ) J_{\frac {\sqrt {a^3+2 b^2}}{2 a^{3/2}}}\left (\frac {\sqrt {a b^2 e^{2 a x} c_2}}{a^{3/2}}\right )\right ){}^2}+c_2\right )\right \}\right \}\] ✗ Maple : cpu = 0. (sec), leaf count = 0
, result contains DESol or ODESolStruc
\[y \relax (x ) = \textit {\_a} \boldsymbol {\mathrm {where}}\left [\left \{\left (\frac {d}{d \textit {\_a}}\mathrm {\_}\mathrm {b}\left (\textit {\_a} \right )\right ) \textit {\_}b\left (\textit {\_a} \right )-\frac {2 b^{2} \textit {\_a}^{3}-2 \textit {\_a}^{2} a^{2}+\textit {\_a} \textit {\_}b\left (\textit {\_a} \right ) a +\textit {\_}b\left (\textit {\_a} \right )^{2}-a \textit {\_a} -\textit {\_}b\left (\textit {\_a} \right )}{\textit {\_a}}=0\right \}, \left \{\textit {\_a} =y \relax (x ), \textit {\_}b\left (\textit {\_a} \right )=\frac {d}{d x}y \relax (x )\right \}, \left \{x =\int \frac {1}{\textit {\_}b\left (\textit {\_a} \right )}d \textit {\_a} +c_{1}, y \relax (x )=\textit {\_a} \right \}\right ]\]