What is the solution for (dy)/(dx)=2+2y+x+xy ?

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

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(dy)/(dx)=2+2y+x+xy

\frac{d y}{d x} = 2 + 2 y + x + x y

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

Solution steps

\frac{d y}{d x} = 2 + 2 y + x + x y

Solve separable ODE:

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

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

f (x) = c x^{- 2}

\frac{\partial}{\partial y} (x y + x^{2})

x y^{^{'}} = y + x^{2} sin (x), y (\frac{π}{4}) = 0

\frac{d}{d x} (\frac{1}{2} e^{\frac{1}{2} x})

x \to + 3 lim (\frac{8}{x - 3})

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