Question

The rate of change of y with respect to x is one-half times the value of y. Find an equation for y, given that when x = 0.
You get:

Please see attachment for answer choices:

Answer 1

"The rate of change of y with respect to x is one-half times the value of y"
means\[\frac{dy}{dx}=\frac12y\]...but that's not a formula for y
so you need to solve this equation by using separation of variables, and determine the value of the constant C based on the given initial condition (which you seem not to have posted)
you only wrote
"given that when x = 0"
there should be a "y=#" after that in order to make this solvable explicitly