What is the solution for (dy)/(dx)=e^{x-y},y(0)=ln(8) ?

The solution for (dy)/(dx)=e^{x-y},y(0)=ln(8) is y=ln(e^x+7)

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(dy)/(dx)=e^{x-y},y(0)=ln(8)

\frac{d y}{d x} = e^{x - y}, y (0) = ln (8)

y = ln (e^{x} + 7)

Solution steps

\frac{d y}{d x} = e^{x - y}

Solve separable ODE:

y = ln (e^{x} + 7)

y = ln (e^{x} + 7)

x \to 0 lim ((1 + 6 x)^{\frac{3}{x}})

\frac{1}{s ^{3} + s}

\int \frac{3 x ^{2} + 7 x + 3}{( x ^{2} + 1 ) ^{2}} d x

\frac{d}{d x} (8^{- x})

x \to 0 lim (\frac{tan ( 3 x )}{x})

What is the solution for (dy)/(dx)=e^{x-y},y(0)=ln(8) ?
The solution for (dy)/(dx)=e^{x-y},y(0)=ln(8) is y=ln(e^x+7)