Final answer:
The question seems to have a miscommunication as the given equation, -y = 5eᴇ₁₀, lacks the components of an initial value problem. An initial value problem requires a differential equation and an initial condition, which are not provided. Clarification is needed to solve the problem correctly.
Step-by-step explanation:
It appears there may be some confusion in the question provided, as it contains several statements that don't seem to relate to a single initial value problem. However, focusing on the given equation, -y = 5eᴇ₁₀ does not express an initial value problem because it lacks both a derivative and an initial condition. For an initial value problem, you would expect to see a differential equation along with an initial condition, such as y(0) = y0.
In order to solve an initial value problem, we would need a differential equation, for example, dy/dt = f(t, y), and an initial condition, say y(t0) = y0. With these, you would integrate the differential equation and apply the initial condition to find the particular solution to the problem.
If your equation is meant to represent a unique context or an equation from a system of equations, then additional information would be necessary to provide an accurate solution. Please clarify the initial conditions and ensure the equation is a differential equation.