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 = 0.226111 (sec), leaf count = 21
\[\left \{\left \{y(x)\to \frac {2 x^3}{1+2 c_1 x^2}\right \}\right \}\]
Maple ✓
cpu = 0.012 (sec), leaf count = 19
\[\left [y \left (x \right ) = \frac {2 x^{3}}{2 x^{2} \textit {\_C1} +1}\right ]\] 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))
Maple raw output
[y(x) = 2*x^3/(2*_C1*x^2+1)]