Find the solution for the initial value problem with initial condition y(0) = yo (0). 52 16 52 y = + -t+ ( yo 27 3 27 27 27 t+ (yo + 52 y = - 52 16 52 4 y = 27 52 4 52 일+(yo le 27 y = - 27 4 52 y = - -t + ( yo 9. 27 Finish solving the equations found in (a) and (b). 16 2 52 + 27 Yo = -- 27 52 16 e 16 + 27 9 Yo = 27 52 9 e4 + 16 3 Yo = - 27 16 2 52 Yo = e 4 27 - 27 52 16 3 + 27 16 Yo e 27 의
Find the solution for the initial value problem with initial condition y(0) = yo (0). 52 16 52 y = + -t+ ( yo 27 3 27 27 27 t+ (yo + 52 y = - 52 16 52 4 y = 27 52 4 52 일+(yo le 27 y = - 27 4 52 y = - -t + ( yo 9. 27 Finish solving the equations found in (a) and (b). 16 2 52 + 27 Yo = -- 27 52 16 e 16 + 27 9 Yo = 27 52 9 e4 + 16 3 Yo = - 27 16 2 52 Yo = e 4 27 - 27 52 16 3 + 27 16 Yo e 27 의
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
Transcribed Image Text:Find the solution for the initial value problem with initial condition y(0) = yo (0).
52
16
52
y =
+
-t+ ( yo
27
3
27
27
27
t+ (yo +
52
y =
-
52
16
52
4
y =
27
52
4
52
일+(yo
le
27
y =
-
27
4
52
y = -
-t + ( yo
9.
27
Finish solving the equations found in (a) and (b).
16 2
52
+
27
Yo
= --
27
52
16
e 16 +
27
9
Yo =
27
52
9
e4 +
16
3
Yo = -
27
16 2
52
Yo =
e 4
27
-
27
52
16
3 +
27
16
Yo
e
27
의
Transcribed Image Text:Consider the initial value problem
y+y=1-. (0) =
= yo -
What equation expresses the requirement that the solution touches the t-axis?
c y(t) = 0
y (t) = 0
O y (t)
= 0
What additional equation expresses the requirement that the solution does not cross the t-axis?
C y' (t) = 0
O y(t) = 0
C y (t) = 0
The equations found in (a) and (b) form a system of two equations for t and yo. Show how the DE can be used to solve directly for t.
3
+Gy = 0, but also 1 –
1
t = 0, so t = 4.
3
y' +
-y = 0, but also 1 - t
1
= 0, so t = 3.
y +
4
= 0, but also 1– zt
1
= 0, so t = 3.
3
4
= 0, but also 1 -
1
= 0, so t = 4.
3
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