ODE
\[ x \left (2 x^3+y(x)\right ) y'(x)=\left (2 x^3-y(x)\right ) y(x) \] ODE Classification
[[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]
Book solution method
Exact equation, integrating factor
Mathematica ✓
cpu = 0.281227 (sec), leaf count = 71
\[\left \{\left \{y(x)\to \frac {2 x^4}{-x+\frac {\sqrt {1+4 c_1 x^4}}{\sqrt {\frac {1}{x^2}}}}\right \},\left \{y(x)\to -\frac {2 x^4}{x+\frac {\sqrt {1+4 c_1 x^4}}{\sqrt {\frac {1}{x^2}}}}\right \}\right \}\]
Maple ✓
cpu = 0.245 (sec), leaf count = 49
\[\left [y \left (x \right ) = \frac {\textit {\_C1} \left (\sqrt {4 x^{4}+\textit {\_C1}^{2}}+\textit {\_C1} \right )}{2 x}, y \left (x \right ) = \frac {\textit {\_C1} \left (2 \textit {\_C1} -2 \sqrt {4 x^{4}+\textit {\_C1}^{2}}\right )}{4 x}\right ]\] Mathematica raw input
DSolve[x*(2*x^3 + y[x])*y'[x] == (2*x^3 - y[x])*y[x],y[x],x]
Mathematica raw output
{{y[x] -> (2*x^4)/(-x + Sqrt[1 + 4*x^4*C[1]]/Sqrt[x^(-2)])}, {y[x] -> (-2*x^4)/(x + Sqrt[1 + 4*x^4*C[1]]/Sqrt[x^(-2)])}}
Maple raw input
dsolve(x*(2*x^3+y(x))*diff(y(x),x) = (2*x^3-y(x))*y(x), y(x))
Maple raw output
[y(x) = 1/2*_C1/x*((4*x^4+_C1^2)^(1/2)+_C1), y(x) = 1/4*_C1/x*(2*_C1-2*(4*x^4+_C1^2)^(1/2))]