What is the solution for (dy)/(dx)=y+y/(xln(x)),y(e)=1 ?

The solution for (dy)/(dx)=y+y/(xln(x)),y(e)=1 is y=e^{x-e}ln(x)

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(dy)/(dx)=y+y/(xln(x)),y(e)=1

\frac{d y}{d x} = y + \frac{y}{x ln ( x )}, y (e) = 1

y = e^{x - e} ln (x)

Solution steps

\frac{d y}{d x} = y + \frac{y}{x ln ( x )}

Solve separable ODE:

y = e^{x - e} ln (x)

y = e^{x - e} ln (x)

\frac{d y}{d x} = - x y, y (0) = 1

y^{^{'}} + y = u, y (0) = \frac{- 1}{2}

\frac{d y}{d x} = \frac{- x}{e ^{y}}

\frac{d x}{d t} = 14 - 0.7 x

\frac{d y}{d x} = \frac{3 sin ( x )}{y}

What is the solution for (dy)/(dx)=y+y/(xln(x)),y(e)=1 ?
The solution for (dy)/(dx)=y+y/(xln(x)),y(e)=1 is y=e^{x-e}ln(x)