Question

Solve the following initial-value differential equations using Laplace and inverse transformation.

y''' +y' =0, y(0)=1, y'(0)=2, y''(0)=1

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

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

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

Differential equations:
Use Laplace transforms to solve:
y’’’ - y’ = 0 , y(0)=0, y’(0)=1, 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

Use the Laplace transform to solve the following initial value
problem
y”+4y=cos(8t)
y(0)=0, y’(0)=0
First, use Y for the Laplace transform of y(t) find the
equation you get by taking the Laplace transform of the
differential equation and solving for Y:
Y(s)=?
Find the partial fraction decomposition of Y(t) and its
inverse Laplace transform to find the solution of the IVP:
y(t)=?

Given the differential equation
y''−2y'+y=0, y(0)=1, y'(0)=2
Apply the Laplace Transform and solve for Y(s)=L{y}
Y(s) =
Now solve the IVP by using the inverse Laplace Transform
y(t)=L^−1{Y(s)}
y(t) =

Solve the following initial value problem using Laplace
transform
y"+2y'+y=4cos(2t) When y(0)=0 y'(0)=2
Thankyou

Solve the initial value problem using Laplace transforms y "+
2ty'-4y = 1; y (0) = y '(0) = 0.

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