Question

Use the method of Laplace Transforms to solve the following IVP.

x'+y'=x-y; x(0)=1

x'-y'=x-y; y(0)=0

Answer #1

Use Laplace transforms to solve the following IVP for the
position function x(t): x'' + 3x' + 2x = 4t, x(0) = 0, x'(0) =
−1

Use Laplace transforms to solve the given IVP
:? ′′ − 9? = 2 + 3?; ?(0) = 0, ?′(0) = 1.

Use the method of laplace transforms to solve the following
Initial Value Problem:
y"+2y'+y=g(t), y'(0)=0

Use the method of Laplace transforms to solve the following
initial value problem. y'' + 6y' + 5y = 12e^t ; y(0) = −1, y'(0) =
7

4.(6)Solve the IVP y” - y = 0, y(0) = 0, y’(0) = 1 by
Laplace transforms. Let Y(s) = LT {y(t)}. Record Y(s) and y(t) on
the lines given.

Use Laplace transforms to solve the following initial value
problem
x'+2y'+x=0, x'-y'+y=0, x(0)=0, y(0)=289
the particular solution is x(t)=? and y(t)= ?

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

Differential equations:
Use Laplace transforms to solve:
y’’’ - y’ = 0 , y(0)=0, y’(0)=1, y’’(0)=2

Use Laplace Transforms to solve the following IVPs .
4y′′+4y′+5y=−t ; y(0)=0 , y′(0)=0

Use Laplace transforms to solve 3y ′′ − 48y = δ(t − 2), y(0) =
1, y ′ (0) = −4.

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