ODE No. 428

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

✓ Mathematica : cpu = 0.0067075 (sec), leaf count = 22

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

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

✓ Maple : cpu = 0.065 (sec), leaf count = 66

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

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