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

ODE
\[ y(x)^2 y'(x)+x (2-y(x))=0 \] ODE Classification

[_separable]

Book solution method
Separable ODE, Neither variable missing

Mathematica
cpu = 26.9186 (sec), leaf count = 38

\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\frac {\text {$\#$1}^2}{2}+2 \text {$\#$1}+4 \log (\text {$\#$1}-2)-6\& \right ]\left [c_1+\frac {x^2}{2}\right ]\right \}\right \}\]

Maple
cpu = 0.008 (sec), leaf count = 27

\[ \left \{ {\frac {{x}^{2}}{2}}-{\frac { \left (y \relax (x ) \right ) ^{2}}{2}}-2\,y \relax (x ) -4\,\ln \left (y \relax (x ) -2 \right ) +{\it \_C1}=0 \right \} \] Mathematica raw input

DSolve[x*(2 - y[x]) + y[x]^2*y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> InverseFunction[-6 + 4*Log[-2 + #1] + 2*#1 + #1^2/2 & ][x^2/2 + C[1]]}
}

Maple raw input

dsolve(y(x)^2*diff(y(x),x)+x*(2-y(x)) = 0, y(x),'implicit')

Maple raw output

1/2*x^2-1/2*y(x)^2-2*y(x)-4*ln(y(x)-2)+_C1 = 0