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Section 3.4 – Repeated Roots; Reduction of Order

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. Find the general solution of the equation \(y''+2y'+y=0.\)

    \(y=e^{-t}(c_1+c_2t)\)

    To see the full video page and find related videos, click the following link.
    MATH 308 WIR22A V35


  2. Solve the initial value problem \[t^2y''+3ty'-3y=0,\qquad y(1)=3, \quad y'(1)=3/2\]
    given that \(y_1(t)=t\) is a solution of the equation.

    \(y=\dfrac{21}{8}t+\dfrac{3}{8}t^{-3}\)

    To see the full video page and find related videos, click the following link.
    MATH 308 WIR22A V36