1. The first order linear method workflow is described in dx + a(t)x = f(x) dt dx the table to the left. The key step is when i(t): dt dx i(t) dt . + i(t) α (ΐ)x = i(t)f(t) i(t)a(t)x(t) simplifies to (x(t)i(t)) , however if d we calculate this derivative using the product rule (x i(t)) = i(t)f(t) dt x i(t) = S i(t)f(t)dt + C d di a (x(t)i(t)) = i(t) + x(t); , we can see that this dt C di x = i(t) Si(t)f(t)dt + simplification only happens if a(t) * i(t). Solve i(t) dt this first order separable equation to derive the formula for i(t). i(t) =
1. The first order linear method workflow is described in dx + a(t)x = f(x) dt dx the table to the left. The key step is when i(t): dt dx i(t) dt . + i(t) α (ΐ)x = i(t)f(t) i(t)a(t)x(t) simplifies to (x(t)i(t)) , however if d we calculate this derivative using the product rule (x i(t)) = i(t)f(t) dt x i(t) = S i(t)f(t)dt + C d di a (x(t)i(t)) = i(t) + x(t); , we can see that this dt C di x = i(t) Si(t)f(t)dt + simplification only happens if a(t) * i(t). Solve i(t) dt this first order separable equation to derive the formula for i(t). i(t) =
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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Question
![dx
1. The first order linear method workflow is described in
+ a(t)x = f (x)
dt
dx
the table to the left. The key step is when i(t)
+
dt
dx
i(t)
+ i(t)a(t)x = i(t)f(t)
d
dt
i(t)a(t)x(t) simplifies to (x(t)i(t)) , however if
dt
d
we calculate this derivative using the product rule
:(xi(t)) = i(t)f(t)
dt
x i(t) = S i(t)f(t)dt + C
d
(x(t)i(t)) = i(t) + x(t), we can see that this
dt
dt
1
C
-S i(t)f(t)dt +
i(t)
di
X =
simplification only happens if
a(t) * i(t). Solve
i(t)
dt
this first order separable equation to derive the formula for i(t).
i(t) =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3d9747ea-4e67-4156-9289-0dc96263d473%2F71fcfa0b-1789-4010-b038-9e1ce7f1f540%2Fx32icpa_processed.png&w=3840&q=75)
Transcribed Image Text:dx
1. The first order linear method workflow is described in
+ a(t)x = f (x)
dt
dx
the table to the left. The key step is when i(t)
+
dt
dx
i(t)
+ i(t)a(t)x = i(t)f(t)
d
dt
i(t)a(t)x(t) simplifies to (x(t)i(t)) , however if
dt
d
we calculate this derivative using the product rule
:(xi(t)) = i(t)f(t)
dt
x i(t) = S i(t)f(t)dt + C
d
(x(t)i(t)) = i(t) + x(t), we can see that this
dt
dt
1
C
-S i(t)f(t)dt +
i(t)
di
X =
simplification only happens if
a(t) * i(t). Solve
i(t)
dt
this first order separable equation to derive the formula for i(t).
i(t) =
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