Help with differential eqs problem???? (Calculus)

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?

  1. 👍
  2. 👎
  3. 👁
  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.

    1. 👍
    2. 👎
    👤
    bobpursley
  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

    1. 👍
    2. 👎
  3. I actually agree with Bridget. I got the same from the first work done.

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Mathxxx!!!

    1. How many solutions does the equation have? 4x+3=2(2x+9) a.one solution b.no solution c. infinite number of solutions d. impossible to determine 2. How many solutions does the equation have? 4x+19=-9-6x a.one solution b.no

  2. Math

    a) Determine an equation, in simplified form, for the family of cubic functions with zeros 2 +- sqrt5 and 0. b) Determine an equation for the member of the family with graph passing through point (2,20)

  3. Differential Equations

    Consider the differential equation: dy/dt=y/t^2 a) Show that the constant function y1(t)=0 is a solution. b)Show that there are infinitely many other functions that satisfy the differential equation, that agree with this solution

  4. Calc

    Consider the differential equation dy/dx=-2x/y Find the particular solution y =f(x) to the given differential equation with the initial condition f(1) = -1

  1. Math 111

    Use the discriminant to determine the number and type of solutions for the given equation. Either A, B, C, OR D 2x^2 = 7x - 8 A One (repeated) rational solution B Two irrational solutions C Two imaginary solutions D Two rational

  2. Math

    Determine an equation in simplified form, for the family of quadratic functions with zeros -1 -+ √5 and 2 -+ √2 B) determine an equation for the member of the family whose graph has a y intercept of -32

  3. ALGEBRA

    The table below shows two equations: Equation 1 |3x - 1| + 7 = 2 Equation 2 |2x + 1| + 4 = 3 Which statement is true about the solution to the two equations? Equation 1 and equation 2 have no solutions. Equation 1 has no solution

  4. Math

    Determine the general equation for the family of quartic functions having zeros at x=-3/2, x=0, x=1/2 and x=2. Determine an equation for a family;y member whose graph passes through the post (-1,4.5)

  1. Calculus

    Consider the differential equation dy/dx = x^4(y - 2). Find the particular solution y = f(x) to the given differential equation with the initial condition f(0) = 0. Is this y=e^(x^5/5)+4?

  2. math

    Consider the differential equation dy/dx = -1 + (y^2/ x). Let y = g(x) be the particular solution to the differential equation dy/ dx = -1 + (y^2/ x) with initial condition g(4) = 2. Does g have a relative minimum, a relative

  3. Calculus BC

    Let y = f(x) be the solution to the differential equation dy/dx=y-x The point (5,1) is on the graph of the solution to this differential equation. What is the approximation of f(6) if Euler’s Method is used given ∆x = 0.5?

  4. Calculus

    Using separation of variables, solve the following differential equation with initial conditions dy/dx = e^(2x+3y) and y(0) = 1. Hint: use a property of exponentials to rewrite the differential equation so it can be separated

You can view more similar questions or ask a new question.