Mathematics 238 test two solutions Tuesday, May 16, 2006 1. State the t-interval on which a solution to the following dierential equation is guaranteed to exist: (4 t2 )y + 2ty + 6y = ln t and y (1) = 0 and y (1) = 0 Rewrite the equation so that the coeci

Mathematics 238 test two Tuesday, May 16, 2006 1. State the t-interval on which a solution to the following dierential equation is guaranteed to exist: (4 t2 )y + 2ty + 6y = ln t and y (1) = 0 and y (1) = 0
2. Circle each linearly independent set of funct

Mathematics 238 test three due Friday, May 26, 2006 1. Given the initial value problem y + 169y = 0 and y (0) = 0 and y (0) = 1 nd the solution function y (t) determine the amplitude and the period of the solution y (t). nd the rst two positive values at

Mathematics 238 test four Friday, June 9, 2006 1. Simplify each of the following:
(a)
0
t3 e5t est dt
(b) u2 (t4)
(c) the convolution et et
2. Given the function f (t) =
6 if t<3 9 t if 3 t < 5 4 if t5
rewrite the function in terms of unit functions uc

name: Mathematics 238 first test Monday, July 7, 2008
please show your work to get full credit for each problem
1. Is y = e4x a solution to the differential equation y - 5y + 4y = 0 ?
x
2. Is y =
0
cos t2 dt a solution of the initial value problem dy = (x

Mathematics 238 rst test Monday, July 7, 2008 1. Is y = e4x a solution to the dierential equation y 5y + 4y = 0 ? Substitute the proposed solution into the dierential equation: 16e4x 5 4e4x + 4 e4x = 0 So y = e4x is a solution to the dierential equation
x

name: Mathematics 238 test two Tuesday, July 22, 2008
please show your work to get full credit for each problem
17. Find the characteristic equation & the general (real-valued) solution of each of the following linear homogeneous differential equations. 1

Mathematics 238 test two solutions Tuesday, July 22, 2008 17. Find the characteristic equation & the general (real-valued) solution of each of the following linear homogeneous differential equations. 1. y + 25y + 100y = 0 r2 + 25r + 100 = 0 = (r + 20)(r +

Mathematics 238 test three due Monday, August 4, 2008
please show your work to get full credit
1. Given the system
dx dt dy dt
= -x + 6y
= -6x - y
(a) Find the real-valued general solution to the system. (b) Sketch the phase plane (xy-plane) for the

Dierential Equations test one Tuesday, April 25, 2006
x
1. Given the function y = 4+
2
sin s2 ds (b) Calculate
dy . dx
(a) Calculate y (2).
2. Is the function y = x+
1 dy 2 a solution of +y = 3+x2 ? x dx
3. Determine whether each of the following equation

Dierential Equations test one solutions Tuesday, April 25, 2006
x
1. Given the function y = 4+
2
sin s2 ds dy = sin x2 dx
2
(a) Calculate y (2) = 4+
2
sin s2 ds = 4+0 = 4
(b) Calculate
2. Is the function y = x+
1 dy 2 a solution of +y = 3+x2 ? Yes because

Mathematics 238 test four solutions Friday, June 10, 2005
please tell me about any errors
1. Find the function which corresponds to each Laplace transform: function transform (a) 2 (s + 4)3 t
2
apply the translation principle:
2! 2 =3 3 s s 2 (s + 4)3
t2

Mathematics 238 test 3 due Monday, November 25, 2002
note : on-line references to power series may be found on-line at http:/www.sosmath.com/diffeq/series/series03/series03.html
http:/college.hmco.com/mathematics/larson/calculus early/3e/shared/chapter15/

Mathematics 238 test 3 due Monday, November 25, 2002
note : on-line references to power series may be found on-line at http:/www.sosmath.com/diffeq/series/series03/series03.html
http:/college.hmco.com/mathematics/larson/calculus early/3e/shared/chapter15/

Mathematics 238 review problems due Thursday September 30, 2010
please show relevant work to get full credit for each problem
1. Find a continuous solution to each initial value problem dy = 8 sin 2t and y (0) = 3 dt dy = dt 2t if t < 0 sin 2t if t 0 and

Dierential Equations nal exam Friday, June 17, 2005
please show all your work to get full credit for each problem
1. Given the initial value problem (x 2)(x + 3)y + 2xy + 4y = ln(x + 1) and y (0) = 8 and y (0) = 2 (a) For which values of x is a continuous

Dierential Equations test one Monday, April 25, 2005
please show your work in order to get full credit
1. Which of the following dierential equations is linear? (a) d2 x = sin x dt2 (b) x2 y (tan x)y = ex (c) dP = P P2 dt
2. For which values of t is the s

Dierential Equations test two Monday, May 16, 2005
please show your work in order to get full credit
1. For which values of t is the solution to the following dierential equation guaranteed to exist? (t2 9)y + (cos t)y + y = 2t and y (0) = 4 2. Calculate

Dierential Equations test two solutions Monday, May 16, 2005 1. For which values of t is the solution to the following dierential equation guaranteed to exist? (t2 9)y + (cos t)y + y = 2t and y (0) = 4 Rewrite the equation to isolate the highest derivativ

Mathematics 238 test three due Friday, May 27, 2005 1. Given the dierential equation (x2 + 4)y + 3xy + 4y = 0
list the singular points of the equation. for which x-values will a power series solution of the form
ak (x3)k converge?
k=0
2. For which values

Mathematics 238 test four Friday, June 10, 2005
please show all your work to get full credit for each problem
1. Find the function which corresponds to each Laplace transform: 2 (s + 4)3 s+3 2s6 s 6e2s s2 + 9
(a)
(b)
(c)
2. Simplify each of the following:

name: Mathematics 238 test four Wednesday, August 13, 2008
please show your work to get full credit for each problem
1. Sketch a graph of the function f (t) = (1 u2 (t) (2t) + (u2 (t) u4 (t) (6 t) + u5 (t) 2. Calculate the Laplace transform of the f (t) =