4.7.7 \(\left (4-x^2\right ) y'(x)+4 y(x)=(x+2) y(x)^2\)

ODE
\[ \left (4-x^2\right ) y'(x)+4 y(x)=(x+2) y(x)^2 \] ODE Classification

[_rational, _Bernoulli]

Book solution method
The Bernoulli ODE

Mathematica
cpu = 0.0187497 (sec), leaf count = 27

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

Maple
cpu = 0.024 (sec), leaf count = 24

\[ \left \{ \left (y \relax (x ) \right ) ^{-1}-{\frac { \left (\ln \left (2+x \right ) +{\it \_C1} \right ) \left (2+x \right ) }{x-2}}=0 \right \} \] Mathematica raw input

DSolve[4*y[x] + (4 - x^2)*y'[x] == (2 + x)*y[x]^2,y[x],x]

Mathematica raw output

{{y[x] -> (2 - x)/((2 + x)*(C[1] - Log[2 + x]))}}

Maple raw input

dsolve((-x^2+4)*diff(y(x),x)+4*y(x) = (2+x)*y(x)^2, y(x),'implicit')

Maple raw output

1/y(x)-(ln(2+x)+_C1)*(2+x)/(x-2) = 0