4.11.11 \(x^4+x y(x) y'(x)-y(x)^2=0\)

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

[[_homogeneous, `class D`], _rational, _Bernoulli]

Book solution method
The Bernoulli ODE

Mathematica
cpu = 0.00717754 (sec), leaf count = 43

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

Maple
cpu = 0.006 (sec), leaf count = 17

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

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

Mathematica raw output

{{y[x] -> -Sqrt[-x^4 + x^2*C[1]]}, {y[x] -> Sqrt[-x^4 + x^2*C[1]]}}

Maple raw input

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

Maple raw output

x^4-x^2*_C1+y(x)^2 = 0