ODE No. 429

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

✓ Mathematica : cpu = 0.0068773 (sec), leaf count = 30

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

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

✓ Maple : cpu = 0.056 (sec), leaf count = 72

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

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