ODE
\[ x^3 y'(x)=y(x) \left (x^2+y(x)\right ) \] ODE Classification
[[_homogeneous, `class D`], _rational, _Bernoulli]
Book solution method
The Bernoulli ODE
Mathematica ✓
cpu = 0.228254 (sec), leaf count = 17
\[\left \{\left \{y(x)\to \frac {x^2}{1+c_1 x}\right \}\right \}\]
Maple ✓
cpu = 0.013 (sec), leaf count = 15
\[\left [y \left (x \right ) = \frac {x^{2}}{x \textit {\_C1} +1}\right ]\] Mathematica raw input
DSolve[x^3*y'[x] == y[x]*(x^2 + y[x]),y[x],x]
Mathematica raw output
{{y[x] -> x^2/(1 + x*C[1])}}
Maple raw input
dsolve(x^3*diff(y(x),x) = y(x)*(x^2+y(x)), y(x))
Maple raw output
[y(x) = x^2/(_C1*x+1)]