2.477   ODE No. 477

\[ a y(x) y'(x)^2+(2 x-b) y'(x)-y(x)=0 \] Mathematica : cpu = 0.216727 (sec), leaf count = 146


\[\left \{\left \{y(x)\to -\frac {e^{\frac {c_1}{2}} \sqrt {2 b-4 x+e^{c_1}}}{2 \sqrt {a}}\right \},\left \{y(x)\to \frac {e^{\frac {c_1}{2}} \sqrt {2 b-4 x+e^{c_1}}}{2 \sqrt {a}}\right \},\left \{y(x)\to -\sqrt {2} e^{\frac {c_1}{2}} \sqrt {2 a e^{c_1}-b+2 x}\right \},\left \{y(x)\to \sqrt {2} e^{\frac {c_1}{2}} \sqrt {2 a e^{c_1}-b+2 x}\right \}\right \}\] Maple : cpu = 0.548 (sec), leaf count = 622


\[y \relax (x ) = -\frac {-2 x +b}{2 \sqrt {-a}}\]