关键词 > MathR105
Math R105 Spring 2022
发布时间:2022-03-16
Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit
Math R105
Spring 2022
Exam 2 Review Problems
1. Use the Wronskian to show that the functions are linearly independent.
a) 1 =
2,
2 =
−3
b) 1 =
2
,
2 =
−3
c) 1 = 1,
2 = cos 3
,
3 = sin 3
2. First verify that 1,
2, ….
are solutions of the differential equation. Then find a particular solution that satisfies the given initial conditions.
a) 2
′′ + 2
′ − 6
= 0;
1 =
2,
2 =
−3;
(2) = 10,
′(2) = 15
b) ′′ +
′ − 6
= 0;
1 =
2
,
2 =
−3
;
(0) = 7,
′(0) = −1
c) (3) + 9
′ = 0;
1 = 1,
2 = cos 3
,
3 = sin 3
;
(0) = 3;
′(0) = −1,
′′(0) = 2
3. Find the general solution of the differential equation given.
a) 6′′ − 7
′ − 20
= 0
b) (4) − 8
′′ + 16
= 0
c) (4) = 16
d) (3) + 3
′′ − 54
= 0; Given:
=
3
is a solution.
4. Solve the initial value problems.
a) ′′ + 4
= 2
;
(0) = 1,
′(0) = 2
b) ′′ + 9
= sin 2
;
(0) = 1,
′(0) = 0