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

The solution for x(dy)/(dx)+y/(x+1)=x(x+1) is y=(c_{1}(x+1))/x-(x+1}{2x}+\frac{x(x+1))/2

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

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

y = \frac{c _{1} ( x + 1 )}{x} - \frac{x + 1}{2 x} + \frac{x ( x + 1 )}{2}

Solution steps

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

Solve linear ODE:

y = \frac{c _{1} ( x + 1 )}{x} - \frac{x + 1}{2 x} + \frac{x ( x + 1 )}{2}

y = \frac{c _{1} ( x + 1 )}{x} - \frac{x + 1}{2 x} + \frac{x ( x + 1 )}{2}

x \to - 1 lim (\frac{x ^{100}}{1})

\int sin^{2} (\frac{nπ x}{L}) d x

\frac{d}{d x} (1 - (x + 1) e^{- x})

\int \frac{2 x ^{5}}{1 - 6 x ^{6}} d x

f (x) = sin (x)

What is the solution for x(dy)/(dx)+y/(x+1)=x(x+1) ?
The solution for x(dy)/(dx)+y/(x+1)=x(x+1) is y=(c_{1}(x+1))/x-(x+1}{2x}+\frac{x(x+1))/2