Find the general solution of the differential equation:  dydx=4e−y

Sure, here is the step-by-step solution to the differential equation dy/dx = 4e^(-y):

Step 1: Rewrite the differential equation in the separable form. This means we want to isolate the y's and the x's on opposite sides of the equation:

dy/dx = 4e^(-y) can be rewritten as e^y dy = 4 dx.

Step 2: Integrate both sides of the equation:

∫e^y dy = ∫4 dx.

The integral of e^y dy is e^y (since the integral of e^y with respect to y is e^y) and the integral of 4 dx is 4x. So we have:

e^y = 4x + C,

where C is the constant of integration.

Step 3: Solve for y:

y = ln(4x + C).

So, the general solution of the differential equation dy/dx = 4e^(-y) is y = ln(4x + C).