Question

**Solve listed initial value problems by using the Laplace
Transform**:

4. *y*^{ll}*−* *y*^{l}*−* 2*y* =
2
*e*^{−}^{2t}* **y*(0)
= 1*, y** ^{l}*(0) =

Answer #1

Use Laplace transform to solve the following initial value
problem: y '' − 2y '+ 2y = e −t , y(0) = 0 and y ' (0) =
1
differential eq

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

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

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

Use
the Laplace transform to solve:
y’’ + 2y’ + y = e^(2t); y(0) = 0, y’(0) = 0.

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

Using the Laplace transform, solve the system of initial value
problems:
w ′′(t) + y(t) + z(t) = −1
w(t) + y ′′(t) − z(t) = 0
−w ′ (t) − y ′ (t) + z ′′(t) = 0
w(0) = 0, w′ (0) = 1, y(0) = 0, y′ (0) = 0, z(0) = −1, z′ (0) =
1

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

Solve this Initial Value Problem using the Laplace
transform.
x''(t) - 9 x(t) = cos(2t),
x(0) = 1,
x'(0) = 3

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