ODE
\[ x^3 y'(x)=x^2 (y(x)-1)+y(x)^2 \] ODE Classification
[[_homogeneous, `class D`], _rational, _Riccati]
Book solution method
Change of Variable, new dependent variable
Mathematica ✓
cpu = 0.296623 (sec), leaf count = 39
\[\left \{\left \{y(x)\to \frac {x \left (e^{2/x}-e^{2 c_1}\right )}{e^{2/x}+e^{2 c_1}}\right \}\right \}\]
Maple ✓
cpu = 0.036 (sec), leaf count = 17
\[\left [y \left (x \right ) = -\tanh \left (\frac {x \textit {\_C1} -1}{x}\right ) x\right ]\] Mathematica raw input
DSolve[x^3*y'[x] == x^2*(-1 + y[x]) + y[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> ((E^(2/x) - E^(2*C[1]))*x)/(E^(2/x) + E^(2*C[1]))}}
Maple raw input
dsolve(x^3*diff(y(x),x) = x^2*(y(x)-1)+y(x)^2, y(x))
Maple raw output
[y(x) = -tanh((_C1*x-1)/x)*x]