2. Solve the IVP u"(t) = cos² (t), u(0) = 0 = u'(0).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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I am attaching the solution for #1 for reference to question #2
Please, I need help with question #2 only
Transcribed Image Text:2. Solve the IVP
u"(t) = cos² (t), u(0) = 0 = u'(0).
Hint: Use your solution from (1). Also, recall fcos2 x dx =
U(s) =
=
+ sin 2x + C.
4
![1. Consider the IVP
u"(t) = 8(t), _u(0) = 0 = u'(0).
Apply the Laplace transform to solve this equation. The solution is the impulse response function
us(t).
Now Applying the laplace transform
L {ult)} = L {& (+)}
[s²u-suco)-u'lo)] = [²
st
i.e
[s²u-s (0)-(0)] = 0+ [8ct). est
= Sco). eº
[s²ū]
su
قاشی
=) ū= ¼/₁²
Now applying inverse laplace
I'{u} = I'{/3²}
u(t)= t·
= |
Ug() = ✓
Setidl-
]==0
us(t) =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8b5d3f26-cda5-43e5-8223-bfa02258241c%2F08751c9e-1338-4294-806a-e0eb0a62c640%2Ffsiyevo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Consider the IVP
u"(t) = 8(t), _u(0) = 0 = u'(0).
Apply the Laplace transform to solve this equation. The solution is the impulse response function
us(t).
Now Applying the laplace transform
L {ult)} = L {& (+)}
[s²u-suco)-u'lo)] = [²
st
i.e
[s²u-s (0)-(0)] = 0+ [8ct). est
= Sco). eº
[s²ū]
su
قاشی
=) ū= ¼/₁²
Now applying inverse laplace
I'{u} = I'{/3²}
u(t)= t·
= |
Ug() = ✓
Setidl-
]==0
us(t) =
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