4.20.5 \(y(x) y'(x)^2-(x y(x)+1) y'(x)+x=0\)

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

\[ \left \{ \left (y \relax (x ) \right ) ^{2}-{\it \_C1}-2\,x=0,y \relax (x ) ={\frac {{x}^{2}}{2}}+{\it \_C1} \right \} \] 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