
Differential Equations Challenge
Quiz
•
Mathematics
•
University
•
Practice Problem
•
Hard
Hemalatha hemalatha
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10 questions
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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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