ODE
\[ x^2 y'(x)=y(x) (a y(x)+x) \] ODE Classification
[[_homogeneous, `class A`], _rational, _Bernoulli]
Book solution method
The Bernoulli ODE
Mathematica ✓
cpu = 0.236812 (sec), leaf count = 17
\[\left \{\left \{y(x)\to \frac {x}{-a \log (x)+c_1}\right \}\right \}\]
Maple ✓
cpu = 0.016 (sec), leaf count = 17
\[\left [y \left (x \right ) = -\frac {x}{a \ln \left (x \right )-\textit {\_C1}}\right ]\] Mathematica raw input
DSolve[x^2*y'[x] == y[x]*(x + a*y[x]),y[x],x]
Mathematica raw output
{{y[x] -> x/(C[1] - a*Log[x])}}
Maple raw input
dsolve(x^2*diff(y(x),x) = (x+a*y(x))*y(x), y(x))
Maple raw output
[y(x) = -x/(a*ln(x)-_C1)]