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 = 0.239817 (sec), leaf count = 17

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

Maple
cpu = 0.015 (sec), leaf count = 15

\[\left [y \left (x \right ) = \frac {1}{a \ln \left (x \right )+x \textit {\_C1} +a}\right ]\] 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))

Maple raw output

[y(x) = 1/(a*ln(x)+x*_C1+a)]