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

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

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

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

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

Solution steps

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

Solve separable ODE:

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

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

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