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# Mason - Mat 214 - MATH 214 EXAM II STUDY GUIDE - Study Guide

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Mason - Mat 214 - MATH 214 EXAM II STUDY GUIDE - Study Guide

##### Description: Chapter 3: Sections 3.1-3.8; gives you steps on how to solve equations (nonhomogeneous and applications).
This preview shows page 1 of a 4 page document. to view the rest of the content MATH 214: Differential Equations Study Guide Exam II What will be covered on the exam: Chapter 3 o Sections 3.1-3.8 What we are allowed to use (Haja’s Class only!): One-sided sheet with anything we need on it Section 3.1: Linear Homogeneous Equations with Constant Coefficients o Second order linear equation: y '' + p ( t ) y ' + q ( t ) y=g ( t ) Rewrite as the Characteristic Equation: a y ' ' + b y ' + c=0 y’’ represents  r 2 , y ' represents r, and y is a constant o Solve like you would a quadratic equation.
o General solution takes the form:
y ( t ) = 1 ( t ) + 2() o Wronskian: Determinant that tells us about the solution. If  it’s non-zero then there are unique solutions to this
problem
W=1Y ' 2−Y ' 2 o Once you find the general solution, if you are given initial  values, use them to figure out the final equation. Section 3.2: Using Intervals o If you have an initial value problem that has an equation  that takes the form of a S.O.L.E. (above)… Where p, q, and g are continuous on an open interval
I, there is exactly ONE SOLUTION (seen as
y=φ(t) )  to this problem, and that one solution exists
throughout that interval I
See Theorem 3.2.4 in textbook Section 3.3: Complex Roots of Characteristic Equations o Consider 2 nd  order Homogeneous Linear Equation: a y ' ' + b y ' + cy=0 , where a, b, and c are in R

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##### Description: Chapter 3: Sections 3.1-3.8; gives you steps on how to solve equations (nonhomogeneous and applications).
4 Pages 64 Views 51 Unlocks
• Notes, Study Guides, Flashcards + More!
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