4.17.27 \(-(x-y(x)) y(x) y'(x)+y'(x)^2-x y(x)^3=0\)

ODE
\[ -(x-y(x)) y(x) y'(x)+y'(x)^2-x y(x)^3=0 \] ODE Classification

[_separable]

Book solution method
No Missing Variables ODE, Solve for \(y'\)

Mathematica
cpu = 0.00665667 (sec), leaf count = 29

\[\left \{\left \{y(x)\to \frac {1}{x-c_1}\right \},\left \{y(x)\to c_1 e^{\frac {x^2}{2}}\right \}\right \}\]

Maple
cpu = 0.008 (sec), leaf count = 25

\[ \left \{ \left (y \relax (x ) \right ) ^{-1}-x-{\it \_C1}=0,y \relax (x ) ={\it \_C1}\,{{\rm e}^{{\frac {{x}^{2}}{2}}}} \right \} \] Mathematica raw input

DSolve[-(x*y[x]^3) - (x - y[x])*y[x]*y'[x] + y'[x]^2 == 0,y[x],x]

Mathematica raw output

{{y[x] -> (x - C[1])^(-1)}, {y[x] -> E^(x^2/2)*C[1]}}

Maple raw input

dsolve(diff(y(x),x)^2-(x-y(x))*y(x)*diff(y(x),x)-x*y(x)^3 = 0, y(x),'implicit')

Maple raw output

y(x) = _C1*exp(1/2*x^2), 1/y(x)-x-_C1 = 0