\[ -y(x) (y(x)+1) \left (b^2 y(x)^2-a^2\right )+(a y(x)-1) y'(x)+y(x) y''(x)-y'(x)^2=0 \] ✗ Mathematica : cpu = 61.7225 (sec), leaf count = 0
DSolve[-(y[x]*(1 + y[x])*(-a^2 + b^2*y[x]^2)) + (-1 + a*y[x])*Derivative[1][y][x] - Derivative[1][y][x]^2 + y[x]*Derivative[2][y][x] == 0,y[x],x]
, could not solve
DSolve[-(y[x]*(1 + y[x])*(-a^2 + b^2*y[x]^2)) + (-1 + a*y[x])*Derivative[1][y][x] - Derivative[1][y][x]^2 + y[x]*Derivative[2][y][x] == 0, y[x], x]
✗ Maple : cpu = 0. (sec), leaf count = 0
dsolve(diff(diff(y(x),x),x)*y(x)-diff(y(x),x)^2+(-1+a*y(x))*diff(y(x),x)-y(x)*(1+y(x))*(b^2*y(x)^2-a^2)=0,y(x))
, result contains DESol or ODESolStruc
\[y \left (x \right ) = \textit {\_a} \:\& \text {where}\:\left [\left \{\left (\frac {d}{d \textit {\_a}}\textit {\_}b\left (\textit {\_a} \right )\right ) \textit {\_}b\left (\textit {\_a} \right )-\frac {\textit {\_a}^{4} b^{2}+\textit {\_a}^{3} b^{2}-\textit {\_a}^{2} a^{2}-\textit {\_a} \textit {\_}b\left (\textit {\_a} \right ) a -\textit {\_a} \,a^{2}+\textit {\_}b\left (\textit {\_a} \right )^{2}+\textit {\_}b\left (\textit {\_a} \right )}{\textit {\_a}}=0\right \}, \left \{\textit {\_a} =y \left (x \right ), \textit {\_}b\left (\textit {\_a} \right )=\frac {d}{d x}y \left (x \right )\right \}, \left \{x =\int \frac {1}{\textit {\_}b\left (\textit {\_a} \right )}d \textit {\_a} +c_{1}, y \left (x \right )=\textit {\_a} \right \}\right ]\]