Question

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

Answer #1

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

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

Solve the system of differential equations using laplace
transformation
dy/dt-x=0,dx/dt+y=1,x(0)=-1,y(0)=1

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

Solve the following initial-value differential
equations using Laplace and inverse transformation.
y''' +y' =0, y(0)=1, y'(0)=2, y''(0)=1

Solve the following initial-value differential
equations using Laplace and inverse transformation.
y''-y=delta(t-3), y(0)=0,
y'(0)=1

Solve the initial value problem using
Laplace transform theory.
y”-2y’+10y=24t,
y(0)=0,
y'(0)= -1

solve using the laplace transform y''-2y'+y=e^-t , y(0)=0 ,
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)=

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