Question

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) =

Answer #1

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)=?

Use
Laplace transform to solve IVP
2y”+2y’+y=2t , y(0)=1 , y’(0)=-1

Use the Laplace transform to solve the following IVP
y′′ +2y′ +2y=δ(t−5) ,y(0)=1,y′(0)=2,
where δ(t) is the Dirac delta function.

Use laplace transform to solve the given IVP
y''-2y'-48y=0
y(0)=13
y'(0)=6

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

Take the Laplace transform of the following initial value
problem and solve for Y(s)=L{y(t)}: y′′−2y′−35y=S(t)y(0)=0,y′(0)=0
where S is a periodic function defined by S(t)={1,0≤t<1 0,
1≤t<2, and S(t+2)=S(t) for all t≥0. Hint: : Use the formula for
the Laplace transform of a periodic function.
Y(s)=

Use the Laplace transform to solve the following initial value
problem:
y′′ + 8y ′+ 16y = 0
y(0) = −3 , y′(0) = −3
First, using Y for the Laplace transform of y(t)y, i.e., Y=L{y(t)},
find the equation you get by taking the Laplace transform of the
differential equation
__________________________ = 0
Now solve for Y(s) = ______________________________ and write the
above answer in its partial fraction decomposition, Y(s) = A /
(s+a) + B / ((s+a)^2)
Y(s) =...

solve using the laplace transform y''-2y'+y=e^-t , y(0)=0 ,
y'(0)=1

y^''-y^'-2y= e^t , y(0)=0 and y^'(0)=1
Solve by using laplace transform

Consider the initial value problem
y′′+4y=16t,y(0)=8,y′(0)=6.y″+4y=16t,y(0)=8,y′(0)=6.
Take the Laplace transform of both sides of the given
differential equation to create the corresponding algebraic
equation. Denote the Laplace transform of y(t) by Y(s). Do not move
any terms from one side of the equation to the other (until you get
to part (b) below).
Solve your equation for Y(s)
Y(s)=L{y(t)}=__________
Take the inverse Laplace transform of both sides of the
previous equation to solve for y(t)y(t).
y(t)=__________

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