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

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

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

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

y = - 1 - x + x^{2} + c_{1} + 1, y = - x - x^{2} + c_{1} + 1 - 1

Solution steps

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

Solve exact ODE:

y = - 1 - x + x^{2} + c_{1} + 1, y = - x - x^{2} + c_{1} + 1 - 1

y = - 1 - x + x^{2} + c_{1} + 1, y = - x - x^{2} + c_{1} + 1 - 1

4 y^{^{''}} + 9 y^{^{'}} = 0

\frac{\partial}{\partial x} (e^{1 x} cos (2 y))

y^{^{''}} + y = 6 sin (2 t) + 4 t cos (2 t)

\frac{d}{d x} (600000 (0.8)^{x})

y = \frac{4}{ln ( x )}

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