ODE
\[ x^2 y'(x)+y(x) \left (x^2+y(x)^2-x\right )=0 \] ODE Classification
[[_homogeneous, `class D`], _rational, _Bernoulli]
Book solution method
Exact equation, integrating factor
Mathematica ✓
cpu = 0.269887 (sec), leaf count = 42
\[\left \{\left \{y(x)\to -\frac {x}{\sqrt {-1+c_1 e^{2 x}}}\right \},\left \{y(x)\to \frac {x}{\sqrt {-1+c_1 e^{2 x}}}\right \}\right \}\]
Maple ✓
cpu = 0.025 (sec), leaf count = 32
\[\left [y \left (x \right ) = \frac {x}{\sqrt {{\mathrm e}^{2 x} \textit {\_C1} -1}}, y \left (x \right ) = -\frac {x}{\sqrt {{\mathrm e}^{2 x} \textit {\_C1} -1}}\right ]\] Mathematica raw input
DSolve[y[x]*(-x + x^2 + y[x]^2) + x^2*y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -(x/Sqrt[-1 + E^(2*x)*C[1]])}, {y[x] -> x/Sqrt[-1 + E^(2*x)*C[1]]}}
Maple raw input
dsolve(x^2*diff(y(x),x)+(x^2+y(x)^2-x)*y(x) = 0, y(x))
Maple raw output
[y(x) = 1/(exp(2*x)*_C1-1)^(1/2)*x, y(x) = -1/(exp(2*x)*_C1-1)^(1/2)*x]