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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} - 2 y^{^{'}} + 5 y = 0, y (\frac{π}{2}) = 0

\int 4 + x d x

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

(y - x y^{2}) d x + x d y = 0

n = 1 \sum \infty \frac{1}{n ^{2} + n}

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