What is the solution for (dy)/(dx)=4e^{x-y},y(0)=ln(7) ?

The solution for (dy)/(dx)=4e^{x-y},y(0)=ln(7) is y=ln(4e^x+3)

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(dy)/(dx)=4e^{x-y},y(0)=ln(7)

\frac{d y}{d x} = 4 e^{x - y}, y (0) = ln (7)

y = ln (4 e^{x} + 3)

Solution steps

\frac{d y}{d x} = 4 e^{x - y}

Solve separable ODE:

y = ln (4 e^{x} + 3)

y = ln (4 e^{x} + 3)

\frac{d y}{d x} = - \frac{6}{4} x^{5} y^{6}

a x^{^{'}} + b x = 0

x y - 2 y - x + 2 - (x y - 2 x - y + 2) \frac{d y}{d x} = 0

(x^{2} + x - 6) y + (x + 3) y^{^{'}} + (x - 2) y = 0

y - 3 y^{^{'}} - 18 = 0

What is the solution for (dy)/(dx)=4e^{x-y},y(0)=ln(7) ?
The solution for (dy)/(dx)=4e^{x-y},y(0)=ln(7) is y=ln(4e^x+3)