Mathematics

Problem

Consider the differential equation

\dfrac{dy}{dx}=k y

, where

k

is a non-zero constant. a. (a) Solve the differential equation subject to the initial condition

y(0)=A

, where

A>0

. b. (b) Show that for any two positive initial values

A_1\neq A_2

, the graphs of the corresponding solutions do not intersect. c. (c) Explain, using the obtained solution, how the sign of

k

affects the behaviour of

y

x

increases without bound.