Differential Equations Challenge

Differential Equations Challenge

University

10 Qs

quiz-placeholder

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Differential Equations Challenge

Differential Equations Challenge

Assessment

Quiz

Mathematics

University

Hard

Created by

Hemalatha hemalatha

FREE Resource

10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

1. The solution of y" + y' - 2y = 0 is: a) ϕ(x) = C1e-2x + C2ex b) ϕ(x) = (C1 + C2) c) ϕ(x) = C1ex + C2e-x d) ϕ(x) = C1

ϕ(x) = C1e^x + C2e^{-2x}

ϕ(x) = C1e^{-x} + C2e^{2x}

ϕ(x) = C1e^{3x} + C2e^{-3x}

ϕ(x) = C1 + C2e^{x}

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

2. The solution of y" + 16y = 0 is: a) ϕ(x) = (C1 + C2)e2x b) ϕ(x) = C1ei4x + C2e-i4x c) ϕ(x) = (C1 + C2)e5x d) None

ϕ(x) = C1sin(4x) + C2cos(4x)

b) ϕ(x) = C1ei4x + C2e-i4x

ϕ(x) = (C1 + C2)e3x

ϕ(x) = C1e2x + C2e-2x

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

3. If ψ(x) = C1e2x + C2e-3x, find ψ(0) = 0, ψ'(0) = ?

5C1

5C2

-3C2

C1e2

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

4. If ϕ1(x) = x, ϕ2(x) = 1, are they: a) Linearly Independent b) Linearly Dependent c) Independent d) Dependent

d) Unrelated

c) Non-orthogonal

a) Orthogonal

b) Linearly Dependent

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

5. If ϕ1 and ϕ2 are two solutions of L(y) = 0, then if ϕ1, ϕ2 are Linearly Dependent, w(ϕ1, ϕ2) = ? a) 0 b) 1 c) 2 d) 4

-1

3

0

5

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

6. What is the general solution of y" + 4y = 0? a) ϕ(x) = C1cos(2x) + C2sin(2x) b) ϕ(x) = C1e2x + C2e-2x c) ϕ(x) = C1e4x + C2e-4x d) None

a) ϕ(x) = C1cos(2x) + C2sin(2x)

ϕ(x) = C1e3x + C2e-3x

ϕ(x) = C1cos(4x) + C2sin(4x)

ϕ(x) = C1cos(x) + C2sin(x)

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

7. The characteristic equation of y" - 5y' + 6y = 0 is: a) r^2 - 5r + 6 = 0 b) r^2 + 5r + 6 = 0 c) r^2 - 6r + 5 = 0 d) None

a) r^2 - 5r + 6 = 0

r^2 - 4r + 6 = 0

r^2 - 5r - 6 = 0

r^2 + 6r + 5 = 0

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