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 = 0.176787 (sec), leaf count = 29
\[\left \{\left \{y(x)\to c_1 e^{-b x}\right \},\left \{y(x)\to -\frac {a x^2}{2}+c_1\right \}\right \}\]
Maple ✓
cpu = 0.081 (sec), leaf count = 22
\[\left [y \left (x \right ) = -\frac {a \,x^{2}}{2}+\textit {\_C1}, y \left (x \right ) = \textit {\_C1} \,{\mathrm e}^{-b x}\right ]\] 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] -> -1/2*(a*x^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))
Maple raw output
[y(x) = -1/2*a*x^2+_C1, y(x) = _C1*exp(-b*x)]