4.17.30 \(x^4 y(x)^4-x \left (x^2+y(x)^2\right ) y(x) y'(x)+y'(x)^2=0\)

ODE
\[ x^4 y(x)^4-x \left (x^2+y(x)^2\right ) y(x) y'(x)+y'(x)^2=0 \] ODE Classification

[_separable]

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

Mathematica
cpu = 0.00775166 (sec), leaf count = 55

\[\left \{\left \{y(x)\to -\frac {1}{\sqrt {-2 c_1-x^2}}\right \},\left \{y(x)\to \frac {1}{\sqrt {-2 c_1-x^2}}\right \},\left \{y(x)\to c_1 e^{\frac {x^4}{4}}\right \}\right \}\]

Maple
cpu = 0.011 (sec), leaf count = 25

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

DSolve[x^4*y[x]^4 - x*y[x]*(x^2 + y[x]^2)*y'[x] + y'[x]^2 == 0,y[x],x]

Mathematica raw output

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

Maple raw input

dsolve(diff(y(x),x)^2-x*y(x)*(x^2+y(x)^2)*diff(y(x),x)+x^4*y(x)^4 = 0, y(x),'implicit')

Maple raw output

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