APM2611
ASSIGNMENT 2 2024
UNIQUE NO.
DUE DATE: 19 JUNE 2024
, APM2611/101/0/2024
ASSIGNMENT 02
Due date: Wednesday, 19 June 2024
-
ONLY FOR YEAR MODULE
Series solutions, Laplace transforms and Fourier series, solving PDE’s by separation of
variables.
Answer all the questions. Show all your own and personalized workings, you get ZERO
to a question if we see that you have copied someone’s else solution word by word.
If you choose to submit via myUnisa, note that only PDF files will be accepted.
Note that all the questions will be marked therefore, it is highly recommended to attempt all of them.
Question 1
Solve the following DEs.
1.
y000− y = 0
2.
y00− 8y 0 + 15y = 0, y(0) = 1, y0(0) = 5
Question 2
Consider the DE
y00− y 0 − 2y = 10 cos x.
Using the method of undetermined coefficients,
1. find a solution for the homogeneous part of the DE
2. find a particular solution
3. write down the generalsolution for the DE.
13
, Question 3
Consider the DE
y00+ y = sec 2 x.
Using the method of variation of parameters,
1. find a solution for the homogeneous part of the DE,
2. find a particular solution,
3. write down the generalsolution for the DE.
4. Find the generalsolution of the given differentialequation:
(i)
y000− 6y 00+ 12y0 − 8y = 0
(ii)
y000+ 3y 00+ 3y 0 + y = 0
5. Solve the boundary value problem00y+ y = 0, y0(0) = 0, y0( π ) = 2.
2
Question 4
1. Solve the given differentialequations by separation of variables:
dy
(i) e x y = e −y + e−2x−y
dx
dx 2
(ii) y ln |x| = y+1
dy x
dy y2 − 1
2. Solve the initial value problem: = 2 , y(2) = 2
dx x −1
3. Show that the given differentialequations are exact and solve them.
dy
(i) x = 2xe x − y + 6x 2.
dx
(ii) (2xy 2 − 3)dx + (2x 2 y + 4)dy = 0.
4. Solve the following linear DEs:
(i) y 0 + 2xy = (2x + 1)e x .
(ii) y 0 = 2y + x + 1.
14
ASSIGNMENT 2 2024
UNIQUE NO.
DUE DATE: 19 JUNE 2024
, APM2611/101/0/2024
ASSIGNMENT 02
Due date: Wednesday, 19 June 2024
-
ONLY FOR YEAR MODULE
Series solutions, Laplace transforms and Fourier series, solving PDE’s by separation of
variables.
Answer all the questions. Show all your own and personalized workings, you get ZERO
to a question if we see that you have copied someone’s else solution word by word.
If you choose to submit via myUnisa, note that only PDF files will be accepted.
Note that all the questions will be marked therefore, it is highly recommended to attempt all of them.
Question 1
Solve the following DEs.
1.
y000− y = 0
2.
y00− 8y 0 + 15y = 0, y(0) = 1, y0(0) = 5
Question 2
Consider the DE
y00− y 0 − 2y = 10 cos x.
Using the method of undetermined coefficients,
1. find a solution for the homogeneous part of the DE
2. find a particular solution
3. write down the generalsolution for the DE.
13
, Question 3
Consider the DE
y00+ y = sec 2 x.
Using the method of variation of parameters,
1. find a solution for the homogeneous part of the DE,
2. find a particular solution,
3. write down the generalsolution for the DE.
4. Find the generalsolution of the given differentialequation:
(i)
y000− 6y 00+ 12y0 − 8y = 0
(ii)
y000+ 3y 00+ 3y 0 + y = 0
5. Solve the boundary value problem00y+ y = 0, y0(0) = 0, y0( π ) = 2.
2
Question 4
1. Solve the given differentialequations by separation of variables:
dy
(i) e x y = e −y + e−2x−y
dx
dx 2
(ii) y ln |x| = y+1
dy x
dy y2 − 1
2. Solve the initial value problem: = 2 , y(2) = 2
dx x −1
3. Show that the given differentialequations are exact and solve them.
dy
(i) x = 2xe x − y + 6x 2.
dx
(ii) (2xy 2 − 3)dx + (2x 2 y + 4)dy = 0.
4. Solve the following linear DEs:
(i) y 0 + 2xy = (2x + 1)e x .
(ii) y 0 = 2y + x + 1.
14
