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

ODE
\[ x^3 y'(x)=(x+1) y(x)^2 \] ODE Classification

[_separable]

Book solution method
Separable ODE, Neither variable missing

Mathematica
cpu = 0.00951533 (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 = 0.005 (sec), leaf count = 21

\[ \left \{ \left (y \relax (x ) \right ) ^{-1}-{\frac {1}{2\,{x}^{2}}}-{x}^{-1}-{\it \_C1}=0 \right \} \] 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),'implicit')

Maple raw output

1/y(x)-1/2/x^2-1/x-_C1 = 0