4.4.38 \(y(x) (1-a y(x) \log (x))+x y'(x)=0\)

ODE
\[ y(x) (1-a y(x) \log (x))+x y'(x)=0 \] ODE Classification

[_Bernoulli]

Book solution method
The Bernoulli ODE

Mathematica
cpu = 0.00976524 (sec), leaf count = 17

\[\left \{\left \{y(x)\to \frac {1}{a \log (x)+a+c_1 x}\right \}\right \}\]

Maple
cpu = 0.008 (sec), leaf count = 20

\[ \left \{ -a\ln \relax (x ) -a-{\it \_C1}\,x+ \left (y \relax (x ) \right ) ^{-1}=0 \right \} \] Mathematica raw input

DSolve[y[x]*(1 - a*Log[x]*y[x]) + x*y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> (a + x*C[1] + a*Log[x])^(-1)}}

Maple raw input

dsolve(x*diff(y(x),x)+(1-a*y(x)*ln(x))*y(x) = 0, y(x),'implicit')

Maple raw output

-a*ln(x)-a-_C1*x+1/y(x) = 0