ODE
\[ x^3 y'(x)=(x+1) y(x)^2 \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.262843 (sec), leaf count = 24
\[\left \{\left \{y(x)\to \frac {2 x^2}{-2 c_1 x^2+2 x+1}\right \}\right \}\]
Maple ✓
cpu = 0.015 (sec), leaf count = 22
\[\left [y \left (x \right ) = \frac {2 x^{2}}{2 x^{2} \textit {\_C1} +2 x +1}\right ]\] Mathematica raw input
DSolve[x^3*y'[x] == (1 + x)*y[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> (2*x^2)/(1 + 2*x - 2*x^2*C[1])}}
Maple raw input
dsolve(x^3*diff(y(x),x) = (1+x)*y(x)^2, y(x))
Maple raw output
[y(x) = 2*x^2/(2*_C1*x^2+2*x+1)]