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

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

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

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

y = \frac{e ^{2 c_{1}} x ^{2}}{2} + e^{2 c_{1}} x + \frac{e ^{2 c_{1}}}{2} - \frac{1}{2}

Solution steps

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

Solve separable ODE:

y = \frac{e ^{2 c_{1}} x ^{2}}{2} + e^{2 c_{1}} x + \frac{e ^{2 c_{1}}}{2} - \frac{1}{2}

y = \frac{e ^{2 c_{1}} x ^{2}}{2} + e^{2 c_{1}} x + \frac{e ^{2 c_{1}}}{2} - \frac{1}{2}

x^{^{'}} x - 5 x = 25

f (x) = \frac{x}{x + 7}

y^{^{'''}} + y^{^{''}} = x - e^{- x}

\int x sin (\frac{1}{11} x) d x

\frac{\partial}{\partial y} (z^{2} e^{x y})

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