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

The solution for x(x+1)(dy)/(dx)+xy=1,y(e)=1 is y=(ln(x))/(x+1)+e/(x+1)

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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

x \to 6 + lim (\frac{x}{x - 6})

\frac{1}{x ^{2}} 4

\frac{\partial}{\partial x} (\frac{6 x - 8 y}{6 x + 8 y})

\frac{\partial}{\partial y} ((x^{2} + y^{2})^{\frac{1}{2}})

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