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 = 0.167684 (sec), leaf count = 52
\[\left \{\left \{y(x)\to -\sqrt {2} \sqrt {x+c_1}\right \},\left \{y(x)\to \sqrt {2} \sqrt {x+c_1}\right \},\left \{y(x)\to \frac {x^2}{2}+c_1\right \}\right \}\]
Maple ✓
cpu = 0.053 (sec), leaf count = 33
\[\left [y \left (x \right ) = \sqrt {2 x +\textit {\_C1}}, y \left (x \right ) = -\sqrt {2 x +\textit {\_C1}}, y \left (x \right ) = \frac {x^{2}}{2}+\textit {\_C1}\right ]\] 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))
Maple raw output
[y(x) = (2*x+_C1)^(1/2), y(x) = -(2*x+_C1)^(1/2), y(x) = 1/2*x^2+_C1]