Question

Solve the initial-value problem y''+5y'+6y=0, y(0)=1, y′(0)=−1,

using Laplace transforms. When writing your answer limit yourself to showing:

(i) The equation for L(y);

(ii) The partial fraction decomposition;

(iii) The antitransforms that finish the problem.

Answer #1

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

Use Laplace transforms to solve the given initial value
problem.
y"-2y'+5y=1+t y(0)=0 y’(0)=4

Solve the following initial value problem. y(4) − 6y′′′ + 5y′′
= 2x, y(0) = 0, y′(0) = 0, y′′(0) = 0, y′′′(0) = 0.
(not using Laplace)

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

use Laplace transforms to solve the integral for y(t)
y"-6y'+5y=(14-8t)e^t
y(0)=3
y'(0)=-4

Solve the given initial-value problem.
y'' + 5y' −
6y =
12e2x, y(0)
= 1, y'(0) = 1

Solve the initial value problem below using the method of
Laplace transforms. y''-y'-30y=0, y(0) = 4 , y'(0) = 46
y(t) = ?

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 the given initial value problem y''-5y'+6y=0, y(0)=3/5,
y'(0)=1

Solve the initial value problem below using the method of
Laplace transforms. y"+11y'+30y=280e^2t, y(0)=1, y'(0)=32

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