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 = 0.253539 (sec), leaf count = 43
\[\left \{\left \{y(x)\to -\sqrt {-x^4+c_1 x^2}\right \},\left \{y(x)\to \sqrt {-x^4+c_1 x^2}\right \}\right \}\]
Maple ✓
cpu = 0.018 (sec), leaf count = 30
\[\left [y \left (x \right ) = \sqrt {-x^{2}+\textit {\_C1}}\, x, y \left (x \right ) = -\sqrt {-x^{2}+\textit {\_C1}}\, x\right ]\] 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))
Maple raw output
[y(x) = (-x^2+_C1)^(1/2)*x, y(x) = -(-x^2+_C1)^(1/2)*x]