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}

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)