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 = 0.315953 (sec), leaf count = 117
\[\left \{\left \{y(x)\to -\sqrt {-\sqrt {-x^2+c_1{}^2}-c_1}\right \},\left \{y(x)\to \sqrt {-\sqrt {-x^2+c_1{}^2}-c_1}\right \},\left \{y(x)\to -\sqrt {\sqrt {-x^2+c_1{}^2}-c_1}\right \},\left \{y(x)\to \sqrt {\sqrt {-x^2+c_1{}^2}-c_1}\right \}\right \}\]
Maple ✓
cpu = 0.093 (sec), leaf count = 97
\[\left [y \left (x \right ) = -\frac {\sqrt {2 \textit {\_C1} -2 \sqrt {\textit {\_C1}^{2}-4 x^{2}}}}{2}, y \left (x \right ) = \frac {\sqrt {2 \textit {\_C1} -2 \sqrt {\textit {\_C1}^{2}-4 x^{2}}}}{2}, y \left (x \right ) = -\frac {\sqrt {2 \textit {\_C1} +2 \sqrt {\textit {\_C1}^{2}-4 x^{2}}}}{2}, y \left (x \right ) = \frac {\sqrt {2 \textit {\_C1} +2 \sqrt {\textit {\_C1}^{2}-4 x^{2}}}}{2}\right ]\] 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))
Maple raw output
[y(x) = -1/2*(2*_C1-2*(_C1^2-4*x^2)^(1/2))^(1/2), y(x) = 1/2*(2*_C1-2*(_C1^2-4*x^2)^(1/2))^(1/2), y(x) = -1/2*(2*_C1+2*(_C1^2-4*x^2)^(1/2))^(1/2), y(x) = 1/2*(2*_C1+2*(_C1^2-4*x^2)^(1/2))^(1/2)]