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## DIFF EQ & TRANSFMS

by: Ms. Helen Sipes

38

0

2

# DIFF EQ & TRANSFMS MATH 267

Ms. Helen Sipes
ISU
GPA 3.98

Hailiang Liu

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COURSE
PROF.
Hailiang Liu
TYPE
Class Notes
PAGES
2
WORDS
KARMA
25 ?

## Popular in Mathematics (M)

This 2 page Class Notes was uploaded by Ms. Helen Sipes on Sunday September 27, 2015. The Class Notes belongs to MATH 267 at Iowa State University taught by Hailiang Liu in Fall. Since its upload, it has received 38 views. For similar materials see /class/214489/math-267-iowa-state-university in Mathematics (M) at Iowa State University.

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Date Created: 09/27/15
E0 9 F 5 533 7 9 Review Problems a y igy21l y15i b y 662x yy0 07 c y EZJQ d y e w 7 e4 we 7 2w o a y y 7 6y 07 y0 07y 0 5 b y 7 59 6y 07 90 OyyO 1 c y 2y73ylze d yH7y72y314 6 y y smltzgt Show that l 176 are two linearly independent solutions for my 7 I My y 0 Then use the variation of parameters method to nd a spec c solution of 1y i 1 1y y I267 Solve by the Laplace transform method a mu me 2n zltogt 0 M0 0 b I 4x fa 10 M0 0 c I 7 1721 07 10 07 10 2 a y y y smut y0 07 by y 10y 6y F 1 yltogt1 W0 2 gm 1 Mo 0 W0 3 Using eigenvalue method to nd general solution alt 31gt we 13gt MEG 73 Classify the equilibrium point at the origin as unstable7 stable7 or asymp A I 7 totically stablei Verify your ndings by sketching a phase portraiti a 3 2 16 9 cm 8 3 yr 74 l 718 ll 7 76 71 Find a particular solution to x AI z aAlt 5 6 e 72 72 andf at b A lt 4 2gtandfltetgti 712 A z 12 Math 267 Review Sheet Fall2004 ISUz 1 First order Differential Equations Chapter 1 2 7ldentify the types of equations integrable eqs7 saparable eqs7 linear eqs7 exact eqs 7 Substitution methodshomogeneous equation7 Bernouli equation7 y ax by 0 2 Linear Equations of Higher Order Chapter 4 7 Solution structure 7 Homogeneous equations with constant Coefficients 7 Variation of Parameters 7 Method of undetermined coefficients 3 Laplace Transform Methods Chapter 5 7 De nition of Laplace Transform amp lnverse Transform 7 Transformation of Initial Value Problems 7 Some formulas and important properties 7 Solving initial value problem via Laplace Transform 4 Numerical methods Chapter 6 7 Euler s method 7 Runge Kutta Methods 5 Linear Systems of Differential Equation Chapter 7 9 7 Higher order equations amp First order systems 7 The Method of Elimination for solving linear system 7 Matrix and Linear Systems 7 Solution Structure of linear systemz Am ft 7 The Eigenvalue Method for homogeneous Systems 7 Variation of parameters for inhomogeneous system 6 Qualitative analysis of Systems 937 96 Chapter 10 7 The linearization of a nonlinear system 7 Type and Stability of equilibrium points 7 Phase plane analysis

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