Final answer:
The student appears to be confused with differential equations and algebraic equations, mixing them in a single question. The algebraic equation after correcting the provided mathematical expression would result in Y=1940/(1-0.48) to find the value of Y.
Step-by-step explanation:
From the differential equation given, it's clear that the student is dealing with a second-order linear ordinary differential equation (ODE) with constant coefficients. However, the equation provided, 4y+40y+400y=800, is likely incorrect due to a lack of differentiation notation. Also, the initial conditions y(0-)=1 and y(0⁻)=0 do not make sense as they both represent a value at the same point (t=0) but are contradictory.
Ignoring the typos and assuming the equation is a second-order ODE, let's focus on the part of the question that seems to be about working through an algebraic equation. After inserting the term 0.3Y for the tax rate T and simplifying the equation, we end up with Y=1940+0.48Y. Solving for Y would involve isolating Y on one side of the equation,
Y = 1940/(1-0.48)
which will give us the final value of Y once calculated.