What is the solution for (dy)/(dx)+y=yxe^{x+8} ?

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

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(dy)/(dx)+y=yxe^{x+8}

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

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

Solution steps

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

Solve separable ODE:

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

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

y^{^{'}} = 1 - y, y (0) = 0

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

y^{^{'}} = \frac{cos ( x ) e ^{s i n (x)}}{2 y}

\frac{d P}{d t} = 5 Pt, P (1) = 5

cos (y) (2 ln (x) - x^{3}) \frac{d y}{d x} = \frac{2}{x} - 3 x^{2}

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