ODE
\[ x^2 y'(x)=2 y(x) \left (x-y(x)^2\right ) \] ODE Classification
[[_homogeneous, `class G`], _rational, _Bernoulli]
Book solution method
The Bernoulli ODE
Mathematica ✓
cpu = 0.234491 (sec), leaf count = 46
\[\left \{\left \{y(x)\to -\frac {x^2}{\sqrt {\frac {4 x^3}{3}+c_1}}\right \},\left \{y(x)\to \frac {x^2}{\sqrt {\frac {4 x^3}{3}+c_1}}\right \}\right \}\]
Maple ✓
cpu = 0.019 (sec), leaf count = 39
\[\left [y \left (x \right ) = -\frac {3 x^{2}}{\sqrt {12 x^{3}+9 \textit {\_C1}}}, y \left (x \right ) = \frac {3 x^{2}}{\sqrt {12 x^{3}+9 \textit {\_C1}}}\right ]\] Mathematica raw input
DSolve[x^2*y'[x] == 2*y[x]*(x - y[x]^2),y[x],x]
Mathematica raw output
{{y[x] -> -(x^2/Sqrt[(4*x^3)/3 + C[1]])}, {y[x] -> x^2/Sqrt[(4*x^3)/3 + C[1]]}}
Maple raw input
dsolve(x^2*diff(y(x),x) = 2*y(x)*(x-y(x)^2), y(x))
Maple raw output
[y(x) = -3/(12*x^3+9*_C1)^(1/2)*x^2, y(x) = 3/(12*x^3+9*_C1)^(1/2)*x^2]