Question

Consider the differential equation dy/dt=y-t
a) Determine whether the following functions are solutions to the given differential
equation.
y(t) = t + 1 + 2e^t
y(t) = t + 1
y(t) = t + 2
b) When you weigh bananas in a scale at the grocery store, the height h of the
bananas is described by the differential equation d^2h/dt^2=-kh
where k is the spring constant, a constant that depends on the properties of
the spring in the scale. After you put the bananas in the scale, you (cleverly)
observe that the height of the bananas is given by h(t) = 4 sin(3t). What is the
value of the spring constant?

Answer 1

take the derivative of each
a. y'=1+2e^t
b. y'=1
c. y'=1

now put in for y', y-t
looks like a works.

b. h=4sin3t
h'=12cos3t
h"=-36sin3t=-kh=-k*4sin3t
k=9

check that.

Answer 2

I actually got 36 for K. Is this right? =4sin(3t)
h'= 4*3*cos(3t) = 12cos(3t)
h"= 12*3*(-sin(3t)) = -36sin(3t)
h"= -k*h = -36*sin(3t)
=36

Answer 3

I actually agree with Bridget. I got the same from the first work done.