ODE
\[ y'(x) (a x+b y(x))+a b x y(x)+y'(x)^2=0 \] ODE Classification
[_quadrature]
Book solution method
No Missing Variables ODE, Solve for \(y'\)
Mathematica ✓
cpu = 0.00502154 (sec), leaf count = 29
\[\left \{\left \{y(x)\to c_1 e^{-b x}\right \},\left \{y(x)\to c_1-\frac {a x^2}{2}\right \}\right \}\]
Maple ✓
cpu = 0.007 (sec), leaf count = 22
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{-bx}},y \left ( x \right ) =-{\frac {a{x}^{2}}{2}}+{\it \_C1} \right \} \] Mathematica raw input
DSolve[a*b*x*y[x] + (a*x + b*y[x])*y'[x] + y'[x]^2 == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[1]/E^(b*x)}, {y[x] -> -(a*x^2)/2 + C[1]}}
Maple raw input
dsolve(diff(y(x),x)^2+(a*x+b*y(x))*diff(y(x),x)+a*b*x*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = -1/2*a*x^2+_C1, y(x) = _C1*exp(-b*x)