Dif Eq Midterm #2

Card Set Information

Author:
klockhart
ID:
48237
Filename:
Dif Eq Midterm #2
Updated:
2010-11-08 18:43:57
Tags:
math
Folders:

Description:
dif eq midterm
Show Answers:

Home > Flashcards > Print Preview

The flashcards below were created by user klockhart on FreezingBlue Flashcards. What would you like to do?


  1. Upon which principle does reduction of order lie?
    Given a solution to a differential equation y1, the second solution, y2 can be found by multiplying y1 by a function u(x).
  2. What formula is useful for reduction of order?
    • y2(x) = y1(x)∫ e-∫P(x) dx y12 (x) dx
    • (Given y" + P(x)y' + Q(x)y = 0)
  3. For an equation in the form Iy" + Jy' + Ky = sin(x), what form of solution should be proposed for yp if using the method of undetermined coefficients?
    Acos(x) + Bsin(x)
  4. What is the basic equation format of variation of parameters?
    yp = u1y1 + u2y2
  5. In variation of parameters, how do you find u1 and u2?
    u1' = W1/W, u2 = W2/W. Then integrate to find u1 and u2, respectively.
  6. In variation of parameters, what are the formulas for W, W1, and W2?
  7. What does a Cauchy-Euler equation look like?
    ax2 d2y/dx2 + bx dy/dx + cy = 0
  8. What form of equation is ax2 d2y/dx2 + bx dy/dx + cy = 0?
    Cauchy-Euler
  9. How do you set up a Cauchy-Euler equation to be solved?
    • ax2 d2y/dx2 + bx dy/dx + cy = ax2m(m -1)xm-2 + bxmxm-1 + cxm
    • (Comes from y = cxm and then taking derivatives for a and b)
  10. How do you format the solutions of a Cauchy-Euler equation?
    y = c1xm1 + c2xm2 or y = c1xm1 + c2xm1lnx or y = xα(c1cos β lnx + c2sin β lnx)
  11. What are the equations that would be used to solve a spring problem (4 equations)?
    • d2x/dt2 + ω2x = 0, ω2 = k/m
    • x(t) = c1cos ωt + c2sin ωt
    • x(t) = Asin(ωt + ϕ), A = √(c12 + c22), tan ϕ = c1/c2
    • d2x/dt2 + 2λ dx/dt + ω2x = 0
  12. How do you handle the solutions of d2x/dt2 + 2λ dx/dt + ω2x = 0?
    λ2 - ω2 > 0: x(t) = e-λt(c1e

What would you like to do?

Home > Flashcards > Print Preview