Question

Find the Laplace transform Y(s)=L{y} of the solution of the given initial value problem.

y′′+9y={t, 0≤t<1 1, 1≤t<∞, y(0)=3, y′(0)=4

Enclose numerators and denominators in parentheses. For example,
(a−b)/(1+n).

Y(s)=

Answer #1

Find the Laplace transform of the given function:
f(t)=(t-3)u2(t)-(t-2)u3(t),
where uc(t) denotes the Heaviside function, which is 0 for
t<c and 1 for t≥c.
Enclose numerators and denominators in parentheses. For example,
(a−b)/(1+n).
L{f(t)}=
_________________ , s>0

Find the Laplace transform Y(s)=L{y} of the solution of the
given initial value problem.
A. y′′+16y = {1, 0 ≤ t < π
= {0, π ≤ t < ∞, y(0)=3, y′(0)=5
B. y′′ + 4y = { t, 0 ≤ t < 1
= {1, 1 ≤ t < ∞, y(0)=3, y′(0)=3

Solve for Y(s), the Laplace transform of the solution y(t) to
the initial value problem below. y''-9y'+18y=5te^(3t), y(0)=2,
y'(0)=-4

Use the Laplace transform to solve the given initial value
problem.
y′′−8y′−105y=0; y(0)=8, y′(0)= 76
Enclose arguments of functions in parentheses. For example,
sin(2x).

Solve the initial-value problem. y"-6y'+9y=0; y(0)=2,
y'(0)=3
Given that y1=x2 is a solution to y"+(1/x)
y'-(4/x2) y=0, find a second, linearly independent
solution y2.
Find the Laplace transform. L{t2 *
tet}
Thanks for solving!

transform the given initial value problem into an algebraic
equation for Y = L{y} in the s-domain. Then find the Laplace
transform of the solution of the initial value problem.
y'' + 4y = 3e^(−2t) * sin 2t,
y(0) = 2, y′(0) = −1

Take the Laplace transform of the following initial value
problem and solve for Y(s)=L{y(t)}: y′′−2y′−35y=S(t)y(0)=0,y′(0)=0
where S is a periodic function defined by S(t)={1,0≤t<1 0,
1≤t<2, and S(t+2)=S(t) for all t≥0. Hint: : Use the formula for
the Laplace transform of a periodic function.
Y(s)=

transform the given initial value problem into an algebraic
equation for Y=L{y}Y=L{y} in the ss-domain. Then find the Laplace
transform of the solution of the initial value problem.
y′′′+y′′+y′+y=0
y(0)=4 y′(0)=0 ,y′′(0)=−2

transform the given initial value problem into an algebraic
equation for Y=L{y}Y=L{y} in the ss-domain. Then find the Laplace
transform of the solution of the initial value problem.
y′′+2y′−2y=0
y(0)=2, y′(0)=1

Consider the following initial value problem: y′′+49y={2t,0≤t≤7
14, t>7 y(0)=0,y′(0)=0 Using Y for the Laplace transform of
y(t), i.e., Y=L{y(t)}, find the equation you get by taking the
Laplace transform of the differential equation and solve for
Y(s)=

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 18 minutes ago

asked 23 minutes ago

asked 23 minutes ago

asked 23 minutes ago

asked 25 minutes ago

asked 32 minutes ago

asked 36 minutes ago

asked 48 minutes ago

asked 58 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago