Ma 2 practical - Written Homework #6
Due Monday, November 16, 2015 before 4pm
Name (Print):
Please write down the question number at the beginning of your solution. You can use
this sheet as a cover.
1. (10 points) Section 4.3
Determine the general solutions of the given differential equation, by the method of
undetermined coefficients
y 000 − y 00 − y 0 + y = e−t + 3.
(1)
2. (10 points) Section 4.3
Determine the general solutions of the given differential equation, by the method of
undetermined coefficients
y 000 − y 0 = 2sin t.
(2)
3. (10 points) Section 4.4
Use the method of variation of parameters to find the general solution to the given
differential equation
y 000 + y 0 = tan t, 0 < t < π.
(3)
4. (10 points) Section 4.4
Find a particular solution of the equation
x3 y 000 + x2 y 00 − 2xy 0 + 2y = 2x4 , x > 0,
(4)
given that x, x2 and 1/x are solutions of the homogenous equation.
5. (10 points) Section 5.2
Seek power series solution to the given differential equation about the given point x0 ;
find the recurrence relation.
y 00 + xy 0 + 2y = 0, x0 = 0.
(5)
Question:
1
2
3
4
5
Total
Points:
10
10
10
10
10
50
Score: