ODE No. 1707

\[ a y(x) y'(x)+b y(x)^2+y(x) y''(x)-y'(x)^2=0 \] Mathematica : cpu = 0.0664731 (sec), leaf count = 31

DSolve[b*y[x]^2 + a*y[x]*Derivative[1][y][x] - Derivative[1][y][x]^2 + y[x]*Derivative[2][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to c_2 e^{-\frac {b x}{a}-\frac {c_1 e^{-a x}}{a}}\right \}\right \}\] Maple : cpu = 1.037 (sec), leaf count = 39

dsolve(diff(diff(y(x),x),x)*y(x)-diff(y(x),x)^2+a*y(x)*diff(y(x),x)+b*y(x)^2=0,y(x))
 

\[y \left (x \right ) = {\mathrm e}^{\frac {c_{1} {\mathrm e}^{-a x}}{a}} {\mathrm e}^{-\frac {b x}{a}} {\mathrm e}^{-\frac {c_{2}}{a}} {\mathrm e}^{\frac {b}{a^{2}}}\]