MA 221 Homework Solutions
Due date: February 13, 2014
4.4 pg. 182 # 6, 14, 12, 13, 15, 17, 21, 23
(Underlined Problems are to be handed in)
In problem 5 determine whether the method or not the method of undetermined coefficients
can be applied to find a
MA 221 Homework Solutions
Due February 6, 2014
4.3, pg. 173 # 2, 4, 6, 8, 17, 27, 29b
(Underlined problems are to be handed in)
In problems 2, 4, 6 and 8, the auxilliary equation for the given differential equation has
complex roots. Find a general solu
Ma 221 Homework Solutions
Due date: January 30, 2014
2.6 p.74 #21, 23, 28;
4.2 p. 165 - 166 #2, 4, 5, 8, 10, 17, 26, 27 29
(Underlined Problems are to handed in.)
2.6 p.74 # 21, 23, 28
For 21, 23 and 28 use the method discussed under "Bernoulli Equations"
MA 221 Homework Solutions
Due date: January 28, 2014
pg. 61 - 62 Sec. 2.4 #10, 11, 13, 15, 17, 19, 23, 24, 25, 27a, 29
(Underlined Problems are to be turned in.)
In problems 9, 11, 13, 15, 17 and 19, determine whether the equation is exact. If it is, then
Ma 221 Homework Solutions Spring 2014
Due January 16, 2014
1.2 p.13-14 #2, 4, 5, 6, 7, 8, 10, 11, 17, 20b, 21b, 22a,b
2.
dy
(a) Show that x x 2 is an explicit solution to x dx 2y on the interval , .
Differentiating x gives:
x 2x
Substituting and for y an
Ma 221 Homework Solutions Due Date:
January 21, 2014
2.2 pg. 43 # 2, 3, 6, 11, 15, 17 19, 21, 23; (Underlined problems are
handed in)
Page 43
In problems 1, 4 and 5, determine whether the given differential equation is separable.
2)
dy
dx
dy
4y 2 3y1
4y
Ma 221 - Exam II review
Second Order Differential Equations
Form of general solution
yh c1y1 c2y2
where y 1 and y 2 are linearly independent solutions of the homogeneous equation and
y yh yp
where y p is a [particular] so;lution of the non-homogeneous equ
Ma 221 Homework Solutions Due 2/20/14
4.4 Page 182 18 , 19 , 24 , 34
18.
y 4y 8 sin 2t
The characteristic polynomial is pr r 2 4 so the roots are r 2i and therefore
y h c 1 sin 2t c 2 cos 2t
Consider a companion equation
v 4v 8 cos 2t
Multiplying the firs
MA 221 Homework Solutions
Due February 11, 2014
4.2 p. 166 # 37, 43
4.4 p. 182 # 10, 11, 14
(Underlined problems are to be handed in)
Section 4.2
37) For problem 37, find three linearly independent solutions.
y y 6y 4y 0
The auxiliary equation is
r 3 r 2
Name:_
Lecturer _
Lecture Section: _
Ma 221
14F
Exam IA
Solutions
Solve the following differential equations. Characterize your solution as explicit or implicit.
1 25 pts.
y
dy
x 5
dx
y3
Solution: This is a Bernoulli equation. We rewrite it as
dy
y
x 5y
Ma 221 - Differential Equations
Workshop 5 (Solutions)
October 1, 2015
Each group submits a single writeup with their results for Problems 1 and 2.
Include the names of all group members and include the letter of your recitation section.
1. Forcing near r
Ma 221
Workshop 6 (Solutions)
Oct 8, 2015
1. Variation of Parameters. This method works for any linear second-order ODE of the
form, L(y) = y 00 + P (x)y 0 + Q(x)y = f (x). Assume we have two linearly independent
solutions for the homogeneous equation, y1
Ma 221 - Differential Equations
Homework 7 (Solutions)
Due: Mar 23, 2017
Grading: 30 pts for the entire assignment. See each problem for particular points.
t
0t<1
1
1t<2
1. Determine the Laplace Transform for f (t) =
.
(t 3) 2 t < 3
0
3 t < +
Grading: 8
Ma 221 - Differential Equations
Homework 4 (Solutions)
Due: Feb 16, 2017
Grading: 30 pts in total. (Problems # 1, 2, 3, 4). See each problem for scoring details.
1. Verify that the given functions form a fundamental set of solutions for the differential e
Ma 221
Homework 8 (Solutions)
Due: Apr 6, 2017
Grading: 30 pts for the entire assignment. See each problem for particular points.
1. Inverse transforms involving translations in s (Theorem 7.3.1) and t (Theorem 7.3.2).
(a) For Y (s) =
3s
, find the invers
Ma 221 - Differential Equations
Homework 6 (Solutions)
Due: Mar 9, 2017
Grading: 30 pts for the entire assignment. See each problem for particular points.
1. Consider the mass-spring system, with mass m in units of slugs, a damping coefficient of
0.50 lb-
Ma 221
Homework 10 (Solutions)
Due: Apr 20, 2017
Grading: 30 pts for the entire assignment. See each problem for particular points.
1. Fourier cosine and sine series for functions on [0, L].
Consider the function f (x) = x/L defined on the interval 0 < x
Ma 221 - Differential Equations
Homework 6 (Solutions)
Due: Oct 20, 2016
Graders: 30 pts for the entire assignment. See each problem for particular points.
1. The following equation models an unforced mass-spring system with a mass of 0.25 kg, a damping
f
MA 221 Homework Solutions
Due date: March 4, 2014
7.2 pg. 360 # 1, 7, 9, 10, 15, 16, 17, 19
(Underlined problems are to be handed in)
In problems 1, 7 and 9, use Definition 1 to determine the Laplace transform of the given
function.
1.) t
Lts
td
N
lim
MA 221 Homework Solutions
Due date: March 25, 2014
Section 8.2 pg. 434 # 1, 2, 5, 6
(Underlined problems are to be handed in)
1.)
n
n2 1 x 1 n
n0
n1
lim aa n lim
n
n
2 n1 /n 2
1 L
2
2 n /n 1
p 1 2
L
The endpoints of the interval of convergence are
x1
Ma 221 - Differential Equations
Homework 2
Due: Feb 9, 2016
Name (Printed):
Recitation:
Collaborators:
I pledge my honor that I have abided by the Stevens Honor System.
Sign:
General Instructions: Write up solutions to the following set of questions and s
Ma 221
Homework 11 (Solutions)
Due: Nov 24, 2015
1. Fourier cosine and sine series for functions on [0, L].
Consider the function f (x) = x/L defined on the interval 0 x < L.
(a) Derive a Fourier sine series for f . Graph the appropriate extension of f (x
Ma 221
Homework 9 (Solutions)
Due: Nov 10, 2015
1. For the following piecewise functions,
Sketch the graph of g(t).
Express g(t) using the unit step function, U(t a).
Apply Theorem 7.3.2 to find the Laplace Transform, G(s) = Lcfw_g(t).
(
(
1,
0t<2
t2 +
Ma 221 - Differential Equations
1.
Homework 1 (Solutions)
Due: Sept 15, 2015
3
dy
= y2
dt
(a) Solve the initial value problem (IVP) with y(0) = 1.
(b) What is the existence interval for the solution in (a)?
(c) Is the solution in (a) unique? If yes, suppo
Ma 221
Homework 7
Name (Printed):
Due: Mar 31, 2016
Recitation:
Pledge and Sign:
General Instructions: Write up solutions to the following set of questions and submit in recitation on
the date indicated. Please staple this cover sheet to your solution pag