ODE
\[ x y(x) y'(x)^2+(y(x)+x) y'(x)+1=0 \] ODE Classification
[_quadrature]
Book solution method
No Missing Variables ODE, Solve for \(y'\)
Mathematica ✓
cpu = 0.154346 (sec), leaf count = 53
\[\left \{\left \{y(x)\to -\sqrt {2} \sqrt {-x+c_1}\right \},\left \{y(x)\to \sqrt {2} \sqrt {-x+c_1}\right \},\{y(x)\to -\log (x)+c_1\}\right \}\]
Maple ✓
cpu = 0.057 (sec), leaf count = 32
\[\left [y \left (x \right ) = -\ln \left (x \right )+\textit {\_C1}, y \left (x \right ) = \sqrt {\textit {\_C1} -2 x}, y \left (x \right ) = -\sqrt {\textit {\_C1} -2 x}\right ]\] Mathematica raw input
DSolve[1 + (x + y[x])*y'[x] + x*y[x]*y'[x]^2 == 0,y[x],x]
Mathematica raw output
{{y[x] -> -(Sqrt[2]*Sqrt[-x + C[1]])}, {y[x] -> Sqrt[2]*Sqrt[-x + C[1]]}, {y[x] -> C[1] - Log[x]}}
Maple raw input
dsolve(x*y(x)*diff(y(x),x)^2+(x+y(x))*diff(y(x),x)+1 = 0, y(x))
Maple raw output
[y(x) = -ln(x)+_C1, y(x) = (_C1-2*x)^(1/2), y(x) = -(_C1-2*x)^(1/2)]