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

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

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

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

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

Solution steps

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

Solve separable ODE:

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

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

1 + 2 t

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

\int (3 x - \frac{4}{3} x^{\frac{3}{2}}) d x

x \to 1 - lim (arcsin (\frac{1}{x}))

t^{3} - 15 t^{2} + 72 t

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