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}

\frac{d}{d x} (\frac{ln ( x )}{1 + ln ( 2 x )})

\int_{0}^{1} (x^{2} + 1)^{10} (2 x) d x

\frac{d}{d x} (2 tan (x) + tan^{2} (x))

\int e^{- 10 x^{2}} d x

\int_{- 1}^{2} x^{2} d x

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)