Solve the initial-value problem?

Question

Solve the initial-value problem dy/dt=3y(t), y(0)=50. What is the domain of the solution?

Answer 1

dy/y = 3dt

ln|y| = 3t + c

Plug in y(0) = 50,

ln50 = c

y = e^(3t+ln50) = 50 e^(3t)

Since there is no restriction on t, the domain of the solution is all real numbers.