2.477   ODE No. 477

\[ a y(x) y'(x)^2+(2 x-b) y'(x)-y(x)=0 \]

✓ Mathematica : cpu = 0.177223 (sec), leaf count = 142

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

\[\left \{\left \{y(x)\to -\sqrt {2} e^{\frac {c_1}{2}} \sqrt {2 a e^{c_1}+b-2 x}\right \},\left \{y(x)\to \sqrt {2} e^{\frac {c_1}{2}} \sqrt {2 a e^{c_1}+b-2 x}\right \},\left \{y(x)\to -\frac {e^{\frac {c_1}{2}} \sqrt {-2 b+4 x+e^{c_1}}}{2 \sqrt {a}}\right \},\left \{y(x)\to \frac {e^{\frac {c_1}{2}} \sqrt {-2 b+4 x+e^{c_1}}}{2 \sqrt {a}}\right \}\right \}\]

✓ Maple : cpu = 0.503 (sec), leaf count = 622

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

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