What is the solution for (dy)/(dx)=2e^{x-y},y(0)=ln(7) ?

The solution for (dy)/(dx)=2e^{x-y},y(0)=ln(7) is y=ln(2e^x+5)

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(dy)/(dx)=2e^{x-y},y(0)=ln(7)

\frac{d y}{d x} = 2 e^{x - y}, y (0) = ln (7)

y = ln (2 e^{x} + 5)

Solution steps

\frac{d y}{d x} = 2 e^{x - y}

Solve separable ODE:

y = ln (2 e^{x} + 5)

y = ln (2 e^{x} + 5)

y^{^{'}} = \frac{x}{e ^{y}}

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

\frac{d y}{y} + (\frac{1}{x} + 1) d x = 0

3 x y^{^{'}} - 5 y = 0, y (1) = 2

\frac{d y}{d x} = - 6 x^{2} y + 9 x^{2}

What is the solution for (dy)/(dx)=2e^{x-y},y(0)=ln(7) ?
The solution for (dy)/(dx)=2e^{x-y},y(0)=ln(7) is y=ln(2e^x+5)