MTH 2201: Differential Equations & Linear Algebra
Solution to 4f and 3c
Bruno Poggi
Wednesday, October 8 2014
Instructor: Dr. Kovats
Here Ill solve any problems that you want to see written solutions for.
Kovats Problem Sheet: Solve the initial value prob
Homework 4
1
May 16, 2011
1.7
3 Solve
y + y = 0
(0.1)
y (0) = 0
(0.2)
y() = 0
(0.3)
If we guess a solution to equation (0.1) of the form y = erx , we see that y = rerx , and
y = r2 erx , so when we substitute, we get the characteristic equation
y + y = r2
Homework 3
1
May 16, 2011
See the end for a proof of something used in class (exercise 36)!
1.6
3,24 We wish to solve the PDE
y 2 ux + x2 uy = 0,
u = u(x, y)
so we assume that there is a product solution, u(x, y) = X(x)Y (y). Substituting gives us
y 2 X Y
Homework 2
May 16, 2011
1
Recall, the denition of linearity for an operator L[u]:
Denition 0.1 (Linearity of PDE operator). A PDE in operator form, i.e. expressed as L[u] = f
like in class, is linear if for any two solutions u1 and u2 and any real number
Homework 1
1
May 16, 2011
1.1
1 a. 1
b. 2
c. 1
d. 4
e. 5
2e We calculate
ux = ex cos(y) + a
uxx = ex cos(y)
uy = ex sin(y) + b
uyy = ex cos(y)
so
uxx + uyy = ex cos(y) ex cos(y) = 0
3b For u = 7 sin(x ct),
ut = 7c cos(x ct),
ux = 7 cos(x ct)
so
ut + cux =
Scientific method
The scientific method has been
around since the 17th century. It is the
method of procedures that use the
characterization of natural science. When
using the scientific method you need to
have you steps in order. The scientific
method is
MTH 2201: Differential Equations & Linear Algebra
Solutions to Open Questions
Bruno Poggi
Wednesday, October 8 2014
Instructor: Dr. Kovats
1. A large tank is filled to capacity with 500 gallons of pure water. Brine containing 2 pounds of salt
per gallon i
MTH 2201: Differential Equations & Linear Algebra
Solutions to More Questions
Bruno Poggi
Wednesday, October 8 2014
Instructor: Dr. Kovats
Here Ill solve any problems that you want to see written solutions for.
Problem 1.a) from Dr. Kovats Problem Sheet:
MTH 2201: Differential Equations & Linear Algebra
Solutions to Even More Questions
Bruno Poggi
Wednesday, October 8 2014
Instructor: Dr. Kovats
Here Ill solve any problems that you want to see written solutions for.
Problem 2.b) from Dr. Kovats Problem Sh
MTH 2201: Differential Equations & Linear Algebra
Solution to 2f
Bruno Poggi
Wednesday, October 8 2014
Instructor: Dr. Kovats
Here Ill solve any problems that you want to see written solutions for.
Problem 2.f ) from Dr. Kovats Problem Sheet: Describe the
Homework 5
1
May 16, 2011
Note again that having the answer in any and all of these problems is not terribly impressive
from a grading standpoint, which is why we provide solutions: it is knowing and doing the work in
between the problem and answer which