For Problems 45-48, use the Laplace transform to solve the given integral equation.
x
(
t
)
=
2
t
2
+
∫
0
t
sin
[
2
(
t
−
τ
)
]
x
(
τ
)
d
τ
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
Calculate the first six iterates for the equation x = e. When xo = 0.
(3t+t²)sin (2t)dt
Suppose the high tide in Seattle occurs at 1:00 a.m. and 1:00 p.m. at which time the water is 16 feet above the height of low tide. Low tides occur 6 hours after high tides. Suppose there are two high tides and two low tides every day and the height of the tide varies sinusoidally.
(a) Find a formula for the function
y = h(t)
that computes the height of the tide above low tide at time t, where t indicates the number of hours after midnight. (In other words,
y = 0
corresponds to low tide.)
h(t) =
(b) What is the tide height at 11:00 a.m.?_____ft
Chapter 10 Solutions
Differential Equations and Linear Algebra (4th Edition)
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.