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

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

[[_homogeneous, `class G`]]

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

Mathematica
cpu = 0.195719 (sec), leaf count = 47

\[\left \{\left \{y(x)\to -\frac {4 e^{-c_1}}{e^{c_1}-2 x}\right \},\left \{y(x)\to -\frac {e^{-c_1}}{4 e^{c_1}-2 x}\right \}\right \}\]

Maple
cpu = 0.187 (sec), leaf count = 82

\[ \left \{ {x}^{2}+{\frac {x}{y \relax (x ) }\sqrt {{x}^{2} \left (y \relax (x ) \right ) ^{2}-4\,y \relax (x ) }}-2\, \left (y \relax (x ) \right ) ^{-1}-{\it \_C1}=0,{x}^{2} \left (y \relax (x ) \right ) ^{2}+y \relax (x ) \sqrt {{x}^{2} \left (y \relax (x ) \right ) ^{2}-4\,y \relax (x ) }x-2\,y \relax (x ) -{\it \_C1}=0,y \relax (x ) =4\,{x}^{-2} \right \} \] Mathematica raw input

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

Mathematica raw output

{{y[x] -> -4/(E^C[1]*(E^C[1] - 2*x))}, {y[x] -> -(1/(E^C[1]*(4*E^C[1] - 2*x)))}}

Maple raw input

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

Maple raw output

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