20094em3 Exercise 21

Engineering Mathematics 3

SECOD ORDER DIFFERETIAL EQUATIOS

Homogeneous Solution Grade 50% off the total score within the first week after due date. Zero score after the first week. Name : Group: Subject: Topic: Date Due: Date of Submission:

Question 2.1.1 Write out the complementary solution if the roots of the characteristic equation are: i. -2, 3 ii. 0, -1 iii. -1, -1 iv. 2, 2 v. 1 + 3i vi. +2i Question 2.1.2 Find the roots of the following characteristic equations: 2

i.

m − m+ 1 = 0

ii.

− 2⋅ m − m + 1 = 0

iii.

2⋅ m − 4⋅ m = 0

iv.

2m − 4 = 0

v.

2⋅ m + 4 = 0

2

2

2

2

Question 2.1.3 Solve the following equations 3y' + 2y = 0 i. 1 ii.

5

y' + 2y = 0

iii.

y'' + 5⋅ y' + 6⋅ y = 0

iv.

2⋅ y'' − 3⋅ y' = 0

v.

2⋅ y'' + 3⋅ y' = 0

vi.

2⋅ y'' + 3y = 0

vii.

2⋅ y'' − 3⋅ y = 0

20094em3 Exercise 21.mcd

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