4.6.13 \(x^2 y'(x)=y(x) (a y(x)+x)\)

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 = 0.00770743 (sec), leaf count = 17

\[\left \{\left \{y(x)\to \frac {x}{c_1-a \log (x)}\right \}\right \}\]

Maple
cpu = 0.006 (sec), leaf count = 20

\[ \left \{ \left (y \relax (x ) \right ) ^{-1}+{\frac {a\ln \relax (x ) -{\it \_C1}}{x}}=0 \right \} \] 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),'implicit')

Maple raw output

1/y(x)+(a*ln(x)-_C1)/x = 0