What is the solution for (dy)/(dx)=8+8y+x+xy ?

The solution for (dy)/(dx)=8+8y+x+xy is y=e^{8x+(x^2)/2+c_{1}}-1

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(dy)/(dx)=8+8y+x+xy

\frac{d y}{d x} = 8 + 8 y + x + x y

y = e^{8 x + \frac{x ^{2}}{2} + c_{1}} - 1

Solution steps

\frac{d y}{d x} = 8 + 8 y + x + x y

Solve separable ODE:

y = e^{8 x + \frac{x ^{2}}{2} + c_{1}} - 1

y = e^{8 x + \frac{x ^{2}}{2} + c_{1}} - 1

\frac{d}{d y} (\frac{x}{x ^{2} + y ^{2} + 1})

x \to - 2 lim (\frac{5 x - 4}{4 - x})

x \to 0 lim (\frac{1 - cos ( 4 x )}{x})

\int 6 y - x - 4 d y

x \to 2 lim (1 - x)

What is the solution for (dy)/(dx)=8+8y+x+xy ?
The solution for (dy)/(dx)=8+8y+x+xy is y=e^{8x+(x^2)/2+c_{1}}-1