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

The solution for x(x+1)((dy)/(dx))+xy=1 is y=(ln(x))/(x+1)+(c_{1})/(x+1)

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x(x+1)((dy)/(dx))+xy=1

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

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

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

What is the solution for x(x+1)((dy)/(dx))+xy=1 ?
The solution for x(x+1)((dy)/(dx))+xy=1 is y=(ln(x))/(x+1)+(c_{1})/(x+1)