ODE
\[ \left (x^2-y(x)^4\right ) y'(x)=x y(x) \] ODE Classification
[[_homogeneous, `class G`], _rational]
Book solution method
Change of Variable, new independent variable
Mathematica ✓
cpu = 0.639934 (sec), leaf count = 117
\[\left \{\left \{y(x)\to -\sqrt {-\sqrt {c_1^2-x^2}-c_1}\right \},\left \{y(x)\to \sqrt {-\sqrt {c_1^2-x^2}-c_1}\right \},\left \{y(x)\to -\sqrt {\sqrt {c_1^2-x^2}-c_1}\right \},\left \{y(x)\to \sqrt {\sqrt {c_1^2-x^2}-c_1}\right \}\right \}\]
Maple ✓
cpu = 0.017 (sec), leaf count = 31
\[ \left \{ \ln \left ( x \right ) -{\it \_C1}+\ln \left ( {\frac { \left ( y \left ( x \right ) \right ) ^{4}+{x}^{2}}{{x}^{2}}} \right ) -2\,\ln \left ( {\frac {y \left ( x \right ) }{\sqrt {x}}} \right ) =0 \right \} \] Mathematica raw input
DSolve[(x^2 - y[x]^4)*y'[x] == x*y[x],y[x],x]
Mathematica raw output
{{y[x] -> -Sqrt[-C[1] - Sqrt[-x^2 + C[1]^2]]}, {y[x] -> Sqrt[-C[1] - Sqrt[-x^2 + C[1]^2]]}, {y[x] -> -Sqrt[-C[1] + Sqrt[-x^2 + C[1]^2]]}, {y[x] -> Sqrt[-C[1] + Sqrt[-x^2 + C[1]^2]]}}
Maple raw input
dsolve((x^2-y(x)^4)*diff(y(x),x) = x*y(x), y(x),'implicit')
Maple raw output
ln(x)-_C1+ln((y(x)^4+x^2)/x^2)-2*ln(y(x)/x^(1/2)) = 0