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x.diff(x)*y=y*log(y/x) equation

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Numerical solution:

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The solution

You have entered [src] 
//x  for 0 = 1\             
||            |          /y\
|<1  for 1 = 1|*y = y*log|-|
||            |          \x/
\\0  otherwise/
y({xfor 0=11for 1=10otherwise)=ylog⁡(yx)y \left(\begin{cases} x & \text{for}\: 0 = 1 \\1 & \text{for}\: 1 = 1 \\0 & \text{otherwise} \end{cases}\right) = y \log{\left(\frac{y}{x} \right)}
Simplify
The graph
Rapid solution [src] 
y1 = E*re(x) + E*I*im(x)
y1=ere⁡(x)+eiim⁡(x)y_{1} = e \operatorname{re}{\left(x\right)} + e i \operatorname{im}{\left(x\right)} 
y1 = E*re(x) + E*i*im(x)
Sum and product of roots [src] 
sum
E*re(x) + E*I*im(x)
ere⁡(x)+eiim⁡(x)e \operatorname{re}{\left(x\right)} + e i \operatorname{im}{\left(x\right)} 
=
E*re(x) + E*I*im(x)
ere⁡(x)+eiim⁡(x)e \operatorname{re}{\left(x\right)} + e i \operatorname{im}{\left(x\right)} 
product
E*re(x) + E*I*im(x)
ere⁡(x)+eiim⁡(x)e \operatorname{re}{\left(x\right)} + e i \operatorname{im}{\left(x\right)} 
=
E*(I*im(x) + re(x))
e(re⁡(x)+iim⁡(x))e \left(\operatorname{re}{\left(x\right)} + i \operatorname{im}{\left(x\right)}\right) 
E*(i*im(x) + re(x))
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