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

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

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

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

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

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