Question

Use the Laplace transform to solve the ODE, m x ″ + k x = 1 , x ( 0 ) = 0 , x ′ ( 0 ) = 0 , assuming that m and k are positive numbers.

Answer #1

Use laplace transform to solve
x'' + 16x = cos(4t)
x(0)= 0
x'(0)= 1

1.
Solve the following ODE for x(t) in terms of m, k, A, B, and
?.
??̈ + ?? = ????(??) + ????(??)
?(0) = ?̇(0) = 0
2.
Solve the following coupled ODE’s for x(t) and y(t).
?̇ + ?? = 1
?̇ + ?? = 0
?(0) = ?(0) = 0

Use
Laplace transform to solve the given initial-value problem:
x"+16x=cos4t, x(0)=0, x'(0)=1

Use the Laplace transform to solve the system.
x' + y =
t
4x + y' = 0
x(0) = 4, y(0) = 4
x = ?
y = ?

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 Laplace Transform to solve the initial value
problem
x''+2x'+2x=e-t x(0)=x'(0)=0.

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. Use the table of Laplace transforms in Appendix III as
needed.
y'' + 25y = cos 5t, y(0) =
3, y'(0) = 4

Use the definition of the Laplace transform to solve the
IVP:
4y''− 4y' + 5y = δ(t), y(0) = −1, y'(0) = 0.

Solve the system by Laplace Transform:
x'=x-2y
y'=5x-y
x(0)=-1, y(0)=2

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