3. Solve using the Laplace transform: (a) y"+y=03(t), y(0) = 0, y'(0) = 1. (b) y"=t04(t), y(0) = 0, y'(0) = 1. Above, 0(t) = 0(t-c), with 0(t) the Heaviside step-function.
3. Solve using the Laplace transform: (a) y"+y=03(t), y(0) = 0, y'(0) = 1. (b) y"=t04(t), y(0) = 0, y'(0) = 1. Above, 0(t) = 0(t-c), with 0(t) the Heaviside step-function.
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 3 please
![3. Solve using the Laplace transform:
(a)
y"+y=03(t),
(b)
y"=t04(t),
y(0) = 0,
Above, 0(t) = 0(t-c), with 0(t) the Heaviside step-function.
(a)
4. Find the solution in terms of the power series, y(x) = Eo ana" (derive the recurrence
relation for the coefficients):
n=0
Jy" + (2 + x)y=0,
y(0) = 0, y'(0) = 1.
(c)
a0-230]
=
dt y
d
20-80
=
5. Find the general solution and draw the phase portrait in (x, y) plane:
(a)
(b)
dt
y(0) = 0,
d
(b)
V= = x² - x³,
y'(0) = 1.
y'(0) = 1.
(d)
[(3+x)y" + y = 0,
[y(0) = 0, y'(0) = 1.
20-60
dt
6. Find the stationary points for the system
d
x= x(t), v=v(t),
dt
and plot the phase portrait of the linearized system near each of them.
d I
3
10-B 30
=](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F71886d56-a83a-4d7b-8e18-9a0e9bdd4c82%2Fe5865575-2570-42c5-aa1f-3c964f36c2ec%2Fw1x08qi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. Solve using the Laplace transform:
(a)
y"+y=03(t),
(b)
y"=t04(t),
y(0) = 0,
Above, 0(t) = 0(t-c), with 0(t) the Heaviside step-function.
(a)
4. Find the solution in terms of the power series, y(x) = Eo ana" (derive the recurrence
relation for the coefficients):
n=0
Jy" + (2 + x)y=0,
y(0) = 0, y'(0) = 1.
(c)
a0-230]
=
dt y
d
20-80
=
5. Find the general solution and draw the phase portrait in (x, y) plane:
(a)
(b)
dt
y(0) = 0,
d
(b)
V= = x² - x³,
y'(0) = 1.
y'(0) = 1.
(d)
[(3+x)y" + y = 0,
[y(0) = 0, y'(0) = 1.
20-60
dt
6. Find the stationary points for the system
d
x= x(t), v=v(t),
dt
and plot the phase portrait of the linearized system near each of them.
d I
3
10-B 30
=
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