Scroll back to the top

Virtual Math Learning Center Logo

Section 6.4 – Differential Equations with Discontinuous Forcing Functions

Directions. The following are review problems for the section. It is recommended you work the problems yourself, and then click "Answer" to check your answer. If you do not understand a problem, you can click "Video" to learn how to solve it. 
  1. Solve the following initial value problem using the Laplace transform: \[y''+2y'+5y=\sin (t)+u_{\pi}(t)\cos(t-\pi),\qquad y(0)=0, \quad y'(0)=0.\]

    \(y(t)=h(t)+u_{\pi}(t)p(t-\pi)\), where \(h(t)=-\dfrac{1}{10}\cos(t)+\dfrac{2}{10}\sin(t)+e^{-t}[\dfrac{1}{10}\cos(2t)-\dfrac{1}{20}\sin(2t)]\) and \(p(t-\pi)=-\dfrac{2}{10}\cos(t)-\dfrac{1}{10}\sin(t)+e^{-(t-\pi)}[-\dfrac{2}{10}\cos(2t)-\dfrac{3}{20}\sin(2t)]\)

    To see the full video page and find related videos, click the following link.
    MATH 308 WIR22A V58