ODE No. 564

\[ a \left (x y'(x)-y(x)\right )+\log \left (y'(x)\right )=0 \]

✓ Mathematica : cpu = 0.003763 (sec), leaf count = 17

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

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

✓ Maple : cpu = 0.025 (sec), leaf count = 32

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

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