What is the solution for (dy)/(dx)+y/(x^2+x)=x+1 ?

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

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(dy)/(dx)+y/(x^2+x)=x+1

\frac{d y}{d x} + \frac{y}{x ^{2} + x} = x + 1

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

Solution steps

\frac{d y}{d x} + \frac{y}{x ^{2} + 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}

\frac{d}{d x} (2 I n x)

\frac{d}{d x} (3 e^{- 4 x})

\frac{1}{x}, 2

3 sin (- 2 x^{2})

x \to 0 lim ((1 + 2 x)^{\frac{1}{2 x ^{2}}})

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