Solution Examination 1 Differential Equations Section 005
1. A tank initially contains 120 liters of pure water. A mixture containing a concentration of g g/liter enters the tank at a rate of 2 liters/min,
and the well-stirred mixture leaves the tank at t
Review Exam 1 Differential Equations Summer 2013
I.
Series
A. Radius of Convergence
1. Testing for radius convergence using complex numbers
2. Radius of convergence of solution of DE from radii of
convergence of coefficient functions
B. Convergence Tests
Final Review Differential Equations
FINAL EXAM, Friday, August 9, 2013
I.
I.
All previous review sheets
Matrix Exponential eAt
A. Calculation of Matrix Exponential
1. Using eigenvectrs and eigenvalues
a.
Complete set of eigenvectors needed
2. Interpolatin
Solution Quiz 12 Section 003
Use undetermined coefficients to solve y - 2 y - 3 y = 3 t 2 t , yH0L = 1, y H0L = 0.
SOLUTION. Let [email protected] = y - 2 y - 3 y . The characteristic polynomial is l2 - 2 l - 3 l = Hl - 3L Hl + 1L and the general solution of
[email protected] = 0
Solutions Examination 1 Differential Equations Section 003
1.
Water is being pumped into a patients stomach at the rate of 0.5 L per minute to flush out 300 grams of alcohol poisoning. The
excess fluid flows out at the same rate. The stomach holds 3 L. Th
Solution Quiz 12 Section 005
Use undetermined coefficients to solve y - 2 y - 3 y = 3 t - t .
SOLUTION. Let [email protected] = y - 2 y - 3 y . The characteristic polynomial is l2 - 2 l - 3 l = Hl - 3L Hl + 1L and the general solution of
[email protected] = 0 is yh = c1 3 t + c2 -
Review Sheet II Differential Equations
I.
III.
Form of Solutions for Inhomogeneous Second Order Linear Equation L[y] = g(x)
A. Particular solution yp(x)
B. Fundamental set of solutions to the reduced homogeneous equation L[y] = 0
C. General solution as su
Review Sheet I Differential Equations
I.
II.
III.
IV.
V.
VI.
VII.
Separable First Order Differential Equation
A. Solution of separable equations by integration
B. Autonomous differential equations y = p(y)
1.
Pearl-Verlhust Model
a.
Equilibrium
2.
Harvest
Solutions Examination 1 Differential Equations
FOR PROBLEMS 1 AND 2 USE THE FOLLOWING DIFFENTIAL EQUATION y - x y - y = 0 AT THE ORDINARY POINT x = 0.
1.
Find the recurrence relation for the coefficients an of the power series solution of the equation.
SO
Examination 2 SolutionaDifferential Equations Section 005
1. Find the general solution for y - 2 y + 5 y = t cos 2 t using UNDETERMINED COEFFICIENTS.
SOLUTION. The characteristic equation is
r2 - 2 r + 5 = 0
which has roots
r=
2
4 - 20
= 1 2 .
2
So the fu
Final Review Differential Equations
FINAL EXAM, Tuesday, April 23
I.
I.
II.
All previous review sheets
Laplace Transforms
A. Definition
1. Exponentially bounded functions
B. Computation
1. Step functions
2. exponentials
3. sine and cosine
4. tp
a.
Gamma f
Practice Midterm Summer 2013
2 - 2 s
1. Find the inverse Laplace transform of FHsL =
.
s2 - 4
SOLUTION. We have that
-1 J
2 - 2 s
s2 - 4
N HtL = l2 * -1 I
2
s2 - 4
M HtL H2 HtL = l2 * sinh H2 tL u2 HtL = sinhH2 t - 4L u2 HtL
Find the solution of [email protected] = y
Make up Exam Differential Equations Summer 2013
1.
Find y H0L, yH3L H0L, yH4L H0L for the solution yHxL of the differential equation y + x y + y = 0 with initial conditions
yH0L = 1, y H0L = 0 and write down the first 5 terms (i.e. up to and including the