ODE
\[ x^3 y'(x)=y(x) \left (2 x^2+y(x)^2\right ) \] ODE Classification
[[_homogeneous, `class A`], _rational, _Bernoulli]
Book solution method
Homogeneous equation
Mathematica ✓
cpu = 0.218199 (sec), leaf count = 42
\[\left \{\left \{y(x)\to -\frac {x^2}{\sqrt {-x^2+c_1}}\right \},\left \{y(x)\to \frac {x^2}{\sqrt {-x^2+c_1}}\right \}\right \}\]
Maple ✓
cpu = 0.015 (sec), leaf count = 34
\[\left [y \left (x \right ) = \frac {x^{2}}{\sqrt {-x^{2}+\textit {\_C1}}}, y \left (x \right ) = -\frac {x^{2}}{\sqrt {-x^{2}+\textit {\_C1}}}\right ]\] Mathematica raw input
DSolve[x^3*y'[x] == y[x]*(2*x^2 + y[x]^2),y[x],x]
Mathematica raw output
{{y[x] -> -(x^2/Sqrt[-x^2 + C[1]])}, {y[x] -> x^2/Sqrt[-x^2 + C[1]]}}
Maple raw input
dsolve(x^3*diff(y(x),x) = (2*x^2+y(x)^2)*y(x), y(x))
Maple raw output
[y(x) = 1/(-x^2+_C1)^(1/2)*x^2, y(x) = -1/(-x^2+_C1)^(1/2)*x^2]