What is the solution for (dy)/(dx)=(y-1)^2e^{x-7},y(7)=2 ?

The solution for (dy)/(dx)=(y-1)^2e^{x-7},y(7)=2 is y=(e^{x-7})/(e^{x-7)-2}-3/(e^{x-7)-2}

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(dy)/(dx)=(y-1)^2e^{x-7},y(7)=2

\frac{d y}{d x} = (y - 1)^{2} e^{x - 7}, y (7) = 2

y = \frac{e ^{x - 7}}{e ^{x - 7} - 2} - \frac{3}{e ^{x - 7} - 2}

Solution steps

\frac{d y}{d x} = (y - 1)^{2} e^{x - 7}

Solve separable ODE:

y = \frac{e ^{x - 7}}{e ^{x - 7} - 2} - \frac{3}{e ^{x - 7} - 2}

y = \frac{e ^{x - 7}}{e ^{x - 7} - 2} - \frac{3}{e ^{x - 7} - 2}

\frac{d x}{d t} = \frac{1}{x e ^{t + 9 x}}

\frac{d y}{d x} = \frac{x ^{5} y}{16 - x ^{6}}

y^{^{'}} = 0.0175 \cdot 7 - \frac{y}{2000} \cdot 7

y^{^{'}} = \frac{2 y ^{4} - 2}{( 4 x y ^{3} )}

a y - b y^{^{'}} = 0

What is the solution for (dy)/(dx)=(y-1)^2e^{x-7},y(7)=2 ?
The solution for (dy)/(dx)=(y-1)^2e^{x-7},y(7)=2 is y=(e^{x-7})/(e^{x-7)-2}-3/(e^{x-7)-2}