Welcome to Bytelearn!

Let’s check out your problem:

Ty tried to solve the differential equation $\frac{d y}{d x}=\frac{4}{x e^{y}}$. This is his work:$\newline$$$\frac{d y}{d x}=\frac{4}{x e^{y}}$$$\newline$Step $1$: $\quad \int e^{y} d y=\int \frac{4}{x} d x$$\newline$Step $2$: $\quad e^{y}=4 \ln |x|+C$$\newline$Step $3$: $\quad \ln \left(e^{y}\right)=\ln (4 \ln |x|+C)$$\newline$Step $4$: $\quad y=\ln (4 \ln |x|+C)$$\newline$Is Ty's work correct? If not, what is his mistake?$\newline$Choose $1$ answer:$\newline$(A) Ty's work is correct.$\newline$(B) Step $1$ is incorrect. The separation of variables was done incorrectly.$\newline$(C) Step $3$ is incorrect. The right-hand side of the equation should be $\ln (4 \ln |x|)+C$.$\newline$(D) Step $4$ is incorrect. The left-hand side of the equation should be $|y|$.