Question

Differential Equations: Use the Laplace transform to solve the given initial value problem:

y′′ −2y′ +2y=cost;

y(0)=1,

y′(0)=0

Answer #1

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

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

Given use Laplace transform to solve the following systems of
differential equations.
2x' - y' - z' = 0
x' + y' = 4t + 2
y' + z = t2 + 2
SUBJECT = ORDINARY DIFFERENTIAL EQUATIONS
TOPIC = LAPLACE TRANSFORM

Use the Laplace transform to solve the given initial value
problem.
y′′−2y′−143y=0; y(0)=8, y′(0)= 32
Enclose arguments of functions in parentheses. For example,
sin(2x).

Use the Laplace transform to solve the given initial-value
problem. y'' − 7y' + 12y = (t − 1), y(0) = 0, y'(0) = 1

Use the Laplace transform to solve the given initial-value
problem. y'' + y = δ(t − 8π), y(0) = 0, y'(0) = 1

Use the Laplace transform to solve the given initial-value
problem.
y'' + 6y' +
34y = δ(t −
π) + δ(t −
7π), y(0) =
1, y'(0) = 0

Use the Laplace transform to solve the given initial-value
problem.
y'' + 10y' +
41y = δ(t −
π) + δ(t −
7π), y(0) =
1, y'(0) = 0

Use the Laplace transform to solve the given initial-value
problem. Use the table of Laplace transforms in Appendix III as
needed.
y'' + 25y = cos 5t, y(0) =
3, y'(0) = 4

Use the Laplace transform to solve the given initial-value
problem.
y'' − 6y' + 13y = 0, y(0) = 0, y'(0) =
−5
#14 7.3
y(t) ?
please show work and circle the answer

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