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

\frac{d}{d x} ((- 4 x^{2} + 25)^{2})

(- 1, 1), (5, - 1)

\frac{d}{d x} (e^{g (x)})

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

x \to 0 lim (\frac{6 x}{x ^{4}})

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