4.8.2 \(x^3 y'(x)+x^2 y(x) \left (1-x^2 y(x)\right )+20=0\)

ODE
\[ x^3 y'(x)+x^2 y(x) \left (1-x^2 y(x)\right )+20=0 \] ODE Classification

[[_homogeneous, `class G`], _rational, _Riccati]

Book solution method
Riccati ODE, Generalized ODE

Mathematica
cpu = 0.0378869 (sec), leaf count = 27

\[\left \{\left \{y(x)\to \frac {4-5 c_1 x^9}{c_1 x^{11}+x^2}\right \}\right \}\]

Maple
cpu = 0.02 (sec), leaf count = 31

\[ \left \{ \ln \relax (x ) -{\it \_C1}+{\frac {\ln \left ({x}^{2}y \relax (x ) +5 \right ) }{9}}-{\frac {\ln \left ({x}^{2}y \relax (x ) -4 \right ) }{9}}=0 \right \} \] Mathematica raw input

DSolve[20 + x^2*y[x]*(1 - x^2*y[x]) + x^3*y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> (4 - 5*x^9*C[1])/(x^2 + x^11*C[1])}}

Maple raw input

dsolve(x^3*diff(y(x),x)+20+x^2*y(x)*(1-x^2*y(x)) = 0, y(x),'implicit')

Maple raw output

ln(x)-_C1+1/9*ln(x^2*y(x)+5)-1/9*ln(x^2*y(x)-4) = 0