2.1758   ODE No. 1758

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

✓ Mathematica : cpu = 0.386289 (sec), leaf count = 36

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

\[\left \{\left \{y(x)\to \frac {-b+(-(c_1 (a+c) (-x-c_2))){}^{\frac {a}{a+c}}}{a}\right \}\right \}\]

✓ Maple : cpu = 0.081 (sec), leaf count = 42

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

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