What is the solution for y+(x+1)(dy)/(dx)=2x+2,y(0)=2 ?

The solution for y+(x+1)(dy)/(dx)=2x+2,y(0)=2 is y=(x^2)/(x+1)+(2x)/(x+1)+2/(x+1)

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y+(x+1)(dy)/(dx)=2x+2,y(0)=2

y + (x + 1) \frac{d y}{d x} = 2 x + 2, y (0) = 2

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

Solution steps

y + (x + 1) \frac{d y}{d x} = 2 x + 2

Solve linear ODE:

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

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

y^{^{'}} = - 8 x y

\frac{d y}{d x} = e^{2 x - y}

\int - e^{- x} ln (x) d x

(1 + x^{2}) (e^{2 t} d t - e^{x} d x) - (1 + x) d x = 0

\frac{s e ^{- 2 s}}{s ^{2} + 16}

What is the solution for y+(x+1)(dy)/(dx)=2x+2,y(0)=2 ?
The solution for y+(x+1)(dy)/(dx)=2x+2,y(0)=2 is y=(x^2)/(x+1)+(2x)/(x+1)+2/(x+1)