What is the solution for (dy)/(dx)=e^{x-y},y(0)=ln(4) ?

The solution for (dy)/(dx)=e^{x-y},y(0)=ln(4) is y=ln(e^x+3)

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(dy)/(dx)=e^{x-y},y(0)=ln(4)

\frac{d y}{d x} = e^{x - y}, y (0) = ln (4)

y = ln (e^{x} + 3)

Solution steps

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

Solve separable ODE:

y = ln (e^{x} + 3)

y = ln (e^{x} + 3)

\frac{d y}{d x} = \frac{tan ( y )}{x}

5 x^{2} d y = \frac{x ^{4} \cdot e ^{3 x}}{y ^{2}} d x

y^{^{'}} + sin^{2} (x) y = cos^{2} (x) y

\frac{d y}{d x} = 2 y, y (3) = 2 e^{- 2}

y^{^{'}} + \frac{33 y}{3090} - \frac{17}{2} = 0

What is the solution for (dy)/(dx)=e^{x-y},y(0)=ln(4) ?
The solution for (dy)/(dx)=e^{x-y},y(0)=ln(4) is y=ln(e^x+3)