Check that the solution of the autonomous differential equation starting from the initial condition b(0) = 1

Question:

Check that the solution of the autonomous differential equation starting from the initial condition b(0) = 1 is b(t) = et-1. Find b(2) and sketch the solution.
The above exercise compare the behavior of two similar-looking differential equations, the pure-time differential equation dp/dt = t and the autonomous differential equation db/dt = b.