ODE
\[ y'(x)^2+(y(x)+x) y'(x)+x y(x)=0 \] ODE Classification
[_quadrature]
Book solution method
No Missing Variables ODE, Solve for \(y'\)
Mathematica ✓
cpu = 0.0032437 (sec), leaf count = 27
\[\left \{\left \{y(x)\to c_1 e^{-x}\right \},\left \{y(x)\to c_1-\frac {x^2}{2}\right \}\right \}\]
Maple ✓
cpu = 0.008 (sec), leaf count = 20
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{-x}},y \left ( x \right ) =-{\frac {{x}^{2}}{2}}+{\it \_C1} \right \} \] Mathematica raw input
DSolve[x*y[x] + (x + y[x])*y'[x] + y'[x]^2 == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[1]/E^x}, {y[x] -> -x^2/2 + C[1]}}
Maple raw input
dsolve(diff(y(x),x)^2+(x+y(x))*diff(y(x),x)+x*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = -1/2*x^2+_C1, y(x) = _C1*exp(-x)