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 = 0.00559688 (sec), leaf count = 53
\[\left \{\left \{y(x)\to -\sqrt {2} \sqrt {c_1-x}\right \},\left \{y(x)\to \sqrt {2} \sqrt {c_1-x}\right \},\left \{y(x)\to c_1-\log (x)\right \}\right \}\]
Maple ✓
cpu = 0.007 (sec), leaf count = 23
\[ \left \{ \left ( y \left ( x \right ) \right ) ^{2}-{\it \_C1}+2\,x=0,y \left ( x \right ) =-\ln \left ( x \right ) +{\it \_C1} \right \} \] 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),'implicit')
Maple raw output
y(x) = -ln(x)+_C1, y(x)^2-_C1+2*x = 0