4.8.22 \(x^4 y'(x)=y(x) \left (x^3+y(x)\right )\)

ODE
\[ x^4 y'(x)=y(x) \left (x^3+y(x)\right ) \] ODE Classification

[[_homogeneous, `class D`], _rational, _Bernoulli]

Book solution method
The Bernoulli ODE

Mathematica
cpu = 0.00798134 (sec), leaf count = 21

\[\left \{\left \{y(x)\to \frac {2 x^3}{2 c_1 x^2+1}\right \}\right \}\]

Maple
cpu = 0.007 (sec), leaf count = 19

\[ \left \{ \left (y \relax (x ) \right ) ^{-1}-{\frac {1}{2\,{x}^{3}}}-{\frac {{\it \_C1}}{x}}=0 \right \} \] Mathematica raw input

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

Mathematica raw output

{{y[x] -> (2*x^3)/(1 + 2*x^2*C[1])}}

Maple raw input

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

Maple raw output

1/y(x)-1/2/x^3-1/x*_C1 = 0