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

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

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

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

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

Solution steps

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

Solve separable ODE:

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

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

\int \frac{1}{60} x^{3} d x

\int - 9 sec (x) tan (x) - 2 sec^{2} (x) d x

\frac{\partial}{\partial x} (e^{x} - e^{- x})

\frac{d}{d x} (1 - \frac{1}{2 x})

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

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