MATH 238 PROBLEMS IN SECTION 4.8 #36. Corresponding to the term =38B C: oeE-9=BF=38B Corresponding to the term -9=#B C: oeG-9=#BH=38#B
On the other hand C- oe -" / #B -# /$B does not have any component that coincides with any part of C: 's above. Therefor
Review for Final
Note: The only topic which might be on the exam, but is not on this review, is direction elds.
In particular, I decided not to put any questions about systems on the exam. The review over
represents section 7.6 compared to the nal, but th
MATH238 OLD TEST 3 1. (10 pts) A mass weighing 32 lb is attached to a spring hanging from the ceiling, thereby causing the spring to stretch 2 feet up coming to rest at equilibrium. Starting at time > oe ! an external force equal to 0>oe)-9=%> is applied
MATH238 OLD TEST 2
1. "! Solve the initial-value problem: Cww " ' C oe ! C ! oe # and Cw !oe #
C oe #-9=%B " =38%B #
#. "! Find a general solution of the differential equation: Cww w & Cww ' Cw oe!
C oe -" -# /#B -$ /$B
$ "! Find a general solut
MA238 OLD_FINAL EXAM Each problem counts 10 points. .C #B" 1. Solve the initial-value problem. : .B oe &C% " C#oe" Ans. C& C oe B# B ' .C 2 Solve the initial value problem : B .B # C oe B# C"oe# Ans. C oe B# 68B#B # 3. Find all values of 7 such that the f
MATH 238 MATLAB ORIENTATION II: SYSTEMS Numerical Methods applied to higher order differential equations. Le> 's consider the mechanical vibration problem with external force function 0 > J -9=# >: 7Cww ,Cw 5C J -9=# > 5 , Let .C @ and solve for Cww .@ 7
MATH 238 OLD TEST 3 1. Find the Laplace transform of 0 > oe /#> by use of the integral definition of Laplace transform.
2. Use formulas to find the Laplace transforms of the following functions: (a) (b) (c) (d) 0 > oe " /$> # 1> oe /#> =38$> /$> ># 2> oe
ass2_ans MATH238-F02 ANSWER TO LAB ASSIGNMENT 2 QUESTION 1 A. Analytic (symbolic) solution
syms y 'real' y1=dsolve('D2y+y=5*cos(t)','y(0)=0,Dy(0)=1') y1 = 5/2*sin(t)*t+sin(t) t1=0:.01:4*pi; y1=5/2*sin(t1).*t1+sin(t1); B. Numerical solution by use of ode45
MATH 238 ANSWER TO OLD TEST 1 1. (a) ODE, 2nd order, nonlinear (b)
# (b) Equilibrium solutions are C ! C " C & (c) source : C ! C & sink : C " (e) If C! # then 3. B " "# "% "' ") C " "% "*' #() %"!*'
C C" >_
lim C> " 7 # #) %"% '!$*
Math 238 Project
Due by April 26, 2013
Note: You will get credit for the project provided it appears that you made a good faith eort to
answer the questions below. You should fully work one of the two problems, but try to do both!
You can document your wo