ODE
\[ y(x) y'(x)^2-(x y(x)+1) y'(x)+x=0 \] ODE Classification
[_quadrature]
Book solution method
No Missing Variables ODE, Solve for \(y'\)
Mathematica ✓
cpu = 0.0050977 (sec), leaf count = 52
\[\left \{\left \{y(x)\to -\sqrt {2} \sqrt {c_1+x}\right \},\left \{y(x)\to \sqrt {2} \sqrt {c_1+x}\right \},\left \{y(x)\to c_1+\frac {x^2}{2}\right \}\right \}\]
Maple ✓
cpu = 0.007 (sec), leaf count = 24
\[ \left \{ \left ( y \left ( x \right ) \right ) ^{2}-{\it \_C1}-2\,x=0,y \left ( x \right ) ={\frac {{x}^{2}}{2}}+{\it \_C1} \right \} \] Mathematica raw input
DSolve[x - (1 + x*y[x])*y'[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] -> x^2/2 + C[1]}}
Maple raw input
dsolve(y(x)*diff(y(x),x)^2-(1+x*y(x))*diff(y(x),x)+x = 0, y(x),'implicit')
Maple raw output
y(x)^2-_C1-2*x = 0, y(x) = 1/2*x^2+_C1