1. ## derivative/differential

A differential equation is an equation in which some function is related to its own derivative(s). For
each of the following functions, calculate the appropriate derivative, and show that the function
satisfies the indicated differential equation
(a) f(x) = 2e^(−3x), f^1(x) = −3*f(x)
(b) f(t) = Ce^kt, f^1(t) = k*f(t)
(c) f(t) = 1 − e^(−t), f^1(t) = 1 − f(t)

2. Originally Posted by kbutto
A differential equation is an equation in which some function is related to its own derivative(s). For
each of the following functions, calculate the appropriate derivative, and show that the function
satisfies the indicated differential equation
(a) f(x) = 2e^(−3x), f^1(x) = −3*f(x)
(b) f(t) = Ce^kt, f^1(t) = k*f(t)
(c) f(t) = 1 − e^(−t), f^1(t) = 1 − f(t)
In each case, substitute the derivative of the given function into the left hand side of the differential equation and show that the result is equal to the right hand side.