What is the solution to the following differential equation? (Use separation of variables!)

Question

Quizplus · Accepted Answer

The differential equation is: 
$$\frac{dy}{dx} = e^x -y$$
Separating the variables, we get: 
$$\frac{dy}{e^x -y} = dx$$
Integrating both sides, we get: 
$$-\ln|e^x -y| = x + C$$
Solving for y, we get: 
$$y = e^x -Ce^{-x}$$
Using the initial condition, y(0) = 1, we get: 
$$1 = 1 -C \Rightarrow C = 0$$
Therefore, the solution to the differential equation is: 
$$y = e^x$$
which corresponds to choice letter B.

What Is the Solution to the Following Differential Equation? (Use