Question

Given use Laplace transform to solve the following systems of differential equations.

2x' - y' - z' = 0

x' + y' = 4t + 2

y' + z = t^{2} + 2

SUBJECT = ORDINARY DIFFERENTIAL EQUATIONS

TOPIC = LAPLACE TRANSFORM

Answer #1

Use the Laplace transform to solve the given system of
differential equations. dx dt = −x + y dy dt = 2x x(0) = 0, y(0) =
2

Use the Laplace transform to solve the given system of
differential equations. d2x dt2 + d2y dt2 = t2 d2x dt2 − d2y dt2 =
3t x(0) = 8, x'(0) = 0, y(0) = 0, y'(0) = 0

Use the Laplace transform to solve the given system of
differential equations. 2 dx/dt + dy/dt − 2x = 1
dx/dt + dy/dt − 6x − 6y = 2
x(0) = 0, y(0) = 0

Differential Equations: Use the Laplace transform to solve the
given initial value problem:
y′′ −2y′ +2y=cost;
y(0)=1,
y′(0)=0

Use the Laplace transform to solve the given system of
differential equations. dx/dt=x-2y dy/dt=5x-y x(0) = -1, y(0) =
6

Solve the system of differential equations using Laplace
transform:
y'' + x + y = 0
x' + y' = 0
with initial conditions
y'(0) = 0
y(0) = 0
x(0) = 1

Topic: Differential Equations, Laplace Transform, particular
solutions
Please explain what is a Laplace transform, why it works, and
why you must use the integral of e^-st, rather than the Laplace
shortcuts, when solving for a piecewise function (with 2+
equations).

Use the Laplace transform to solve the following initial value
problem:
y′′ + 8y ′+ 16y = 0
y(0) = −3 , y′(0) = −3
First, using Y for the Laplace transform of y(t)y, i.e., Y=L{y(t)},
find the equation you get by taking the Laplace transform of the
differential equation
__________________________ = 0
Now solve for Y(s) = ______________________________ and write the
above answer in its partial fraction decomposition, Y(s) = A /
(s+a) + B / ((s+a)^2)
Y(s) =...

Use the Laplace Transform method to solve the following
differential equation problem: y 00(t) − y(t) = t + sin(t), y(0) =
0, y0 (0) = 1
Please show partial fraction steps to calculate
coeffiecients.

Use Laplace transform to solve the following initial value
problem: y '' − 2y '+ 2y = e −t , y(0) = 0 and y ' (0) =
1
differential eq

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