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

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

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

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

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

Solution steps

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

Solve separable ODE:

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

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

\frac{\partial}{\partial y} (x^{2} \cdot y^{3})

\frac{4 x ^{3} + 2 x + 5}{x}

x \to 0 lim (\frac{5 ^{x} - 3 ^{x}}{x})

\int (- x^{5} + 6 e^{- 2 x}) d x

(x + y) y^{^{'}} = x - y

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