Exam # 2 - Solutions Math 308.200 Spring 2002 Name: Student ID:
Signature:
The following exam consists of 8 problems, worth a total of 100 points. There is a total of 10 extra credit points. Partial c
Solutions to Homework from Section 2.3
Problem 6 The equation can be re-written as
dr
= 3r + 3
d
The equation is linear (in r) but not seperable.
Problem 9 The equation is already in standard form
dr
Solutions to Homework from Section 3.4
Problem 18 Assuming the force due to (sliding) friction is proportional to the normal force, the equations of motion of an object sliding down an inclined plane
Final Exam - Solutions Math 308.200 Spring 2002 Name: Signature: The following exam consists of 11 problems, worth a total of 200 points. There is a total of 10 extra credit points. Partial credit wil
Exam # 3 - Solutions Math 308.200 Spring 2002 Name: Student ID:
Signature: The following exam consists of 6 problems, worth a total of 100 points. There is a total of 15 extra credit points. Partial c
Solutions to Homework from Section 1.5
Problem 5 Applying Eulers method (euler.m) gives the following results xn 1.0000 1.2000 1.4000 1.6000 1.8000 yn 1.0000 1.4000 1.9600 2.7888 4.1096
Problem 12 Giv
Solutions to Homework from Section 1.1
Problem 15 From the statement of the problem dT (M - T (t) dt which means that dT = k(M - T (t) dt
for some constant k. Problem 16 In a similar fashion to 15, dA
Exam # 1 Math 308.200 Spring 2002 Name: Student ID:
Signature:
The following exam consists of 6 problems, worth a total of 100 points. Partial credit will be awarded according to the completeness of w
Solutions to Homework from Section 4.7
Problem 13 a) The difference of any two particular solutions is a homogeneous solution, therefore y1 (x) = x3 - x and y2 (x) = x2 - x are homogeneous solutions.
Solutions to Homework from Section 4.10
Problem 4 We show that y1 (t) = 1/(1 - t)2 , y2 (t) = 1/(2 - t)2 , and y3 (t) = 1/(3 - t)2 are independent by computing the Wronskian y1 y2 y3 W = y1 y2 y3 y1 y
Solutions to Homework from Section 9.6
Problem 3 The matrix has eigenvector/eigenvalue pairs equal to 1 0 1 = 1, u1 = 0 -1 - 2i 1 2 = 1 + i, u2 = i -1 + 2i 1 3 = 1 - i, u3 = -i The general solution is
Solutions to Homework from Section 9.4
Problem 9 With x = [x1 , x2 ]T ,
x1
x2
=
5 0
2 4
x1
x2
=
2e2t
3e2t
5x1 + 2e2t
2x1 + 4x2 3e2t
+
Therefore, the matrix system is equivalent to the 2 scalar equatio
Solutions to Homework from Section 5.5
Problem 10
Using Khirchoffs law on the left loop we get
20 = 10I3 (t) + 10I1 (t)
Using Khirchoffs law on the right loop we get
0 = 40I2 (t) + 30I2 (t) 10I3 (t)
T
Solutions to Homework from Section 9.1
Problem 7 The damped mass-spring oscillator equation
my (x) + by (x) + ky(x) = 0
can be written as a matrix ode in normal form by using the change of variables
y
Solutions to Homework from Section 4.4
Problem 6 Given one solution, y1 = ex , find a second solution y2 (x), to the differential equation: xy + (1 - 2x)y + (x - 1)y = 0, x > 0 Substituting the form y
Solutions to Homework from Section 5.2
Problem 18 The critical points are given by solving
x(7 x 2y) = 0
y(5 x y) = 0
which gives cfw_(0,0),(0,5),(7,0),(3,2).
The phase plane, with direction elds in t