c) d² y dt² +2 dy dt + y = 4t, y(0) = 0, y'(0)=5

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Question
5c : using the Laplace transform method
5. Solve the equation subject to the given conditions.
d'y dy
dt
-6y=5e', y(0) = 0, y'(0)=1
dt²
a)
b)
c)
d)
e)
f)
d'y
dt²
h)
d² y
dt²
d² y
dt²
dy
dt
dy
+2. - + y = 4t, y(0) = 0, y'(0)= 5
dt
-6y=4e², y(0) = 1, y'(0)= 4
d² y
dt²
-6y=5U, (t), y(0) = 2
+4y= te³¹, y(0) = 0, y'(0)=1
d² y
dt²
d'y
g) --y=U₁(t)-U₂ (t), y(0) = 0, y'(0)=2
dt²
- y = U₁(t), y(0) = 1, y'(0) = 4
+y = t-U₁(t)(t-1), y(0) = 1, y'(0)=1
Transcribed Image Text:5. Solve the equation subject to the given conditions. d'y dy dt -6y=5e', y(0) = 0, y'(0)=1 dt² a) b) c) d) e) f) d'y dt² h) d² y dt² d² y dt² dy dt dy +2. - + y = 4t, y(0) = 0, y'(0)= 5 dt -6y=4e², y(0) = 1, y'(0)= 4 d² y dt² -6y=5U, (t), y(0) = 2 +4y= te³¹, y(0) = 0, y'(0)=1 d² y dt² d'y g) --y=U₁(t)-U₂ (t), y(0) = 0, y'(0)=2 dt² - y = U₁(t), y(0) = 1, y'(0) = 4 +y = t-U₁(t)(t-1), y(0) = 1, y'(0)=1
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