First-Order Equations · Challenge problem

A fund earns interest at $5\%$ per year, compounded continuously, and pays out money continuously at the growing rate $1000e^{0.03t}$ dollars per year ($t$ in years). Its balance therefore obeys $A'=0.05A-1000e^{0.03t}$. What is the smallest initial balance $A(0)$, in dollars, for which the balance never becomes negative?