4.5.28 \((x+1) y'(x)+(x+1)^4 y(x)^3+y(x)=0\)

ODE
\[ (x+1) y'(x)+(x+1)^4 y(x)^3+y(x)=0 \] ODE Classification

[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli]

Book solution method
The Bernoulli ODE

Mathematica
cpu = 0.0129206 (sec), leaf count = 49

\[\left \{\left \{y(x)\to -\frac {1}{\sqrt {(x+1)^2 \left (c_1+x^2+2 x\right )}}\right \},\left \{y(x)\to \frac {1}{\sqrt {(x+1)^2 \left (c_1+x^2+2 x\right )}}\right \}\right \}\]

Maple
cpu = 0.007 (sec), leaf count = 23

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

DSolve[y[x] + (1 + x)^4*y[x]^3 + (1 + x)*y'[x] == 0,y[x],x]

Mathematica raw output

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

Maple raw input

dsolve((1+x)*diff(y(x),x)+y(x)+(1+x)^4*y(x)^3 = 0, y(x),'implicit')

Maple raw output

1/y(x)^2-(x^2+_C1+2*x)*(1+x)^2 = 0