4.7.50 \(x^3 y'(x)=x^2 (y(x)-1)+y(x)^2\)

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 = 0.0298685 (sec), leaf count = 39

\[\left \{\left \{y(x)\to \frac {x \left (e^{2/x}-e^{2 c_1}\right )}{e^{2 c_1}+e^{2/x}}\right \}\right \}\]

Maple
cpu = 0.008 (sec), leaf count = 19

\[ \left \{ -{\it Artanh} \left ({\frac {y \relax (x ) }{x}} \right ) +{x}^{-1}-{\it \_C1}=0 \right \} \] 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),'implicit')

Maple raw output

-arctanh(y(x)/x)+1/x-_C1 = 0