Solve differential equation using Laplace Transforms. y'' - 6y' + 5y = te^t , y(0) = 2 , y'(0) = -1

Question.


Solve differential equation using Laplace Transforms.

y'' - 6y' + 5y = te^t , y(0) = 2 , y'(0) = -1

Solution:

Solve by using Laplace Transforms. y'''' - 9y = 0 , y(0) = 1, y'(0) = 0 , y''(0) = 0 , y'''(0) = 1

Question. Solve by using Laplace Transforms.
y'''' - 9y = 0 , y(0) = 1, y'(0) = 0 , y''(0) = 0 , y'''(0) = 1

Solution:

Use Eigenvalues and Eigenvectors to find the general solution of the following system of differential equations: y1' = 4y1 + 5y2 ; y2' = -2y1 + 6y2

Use Eigenvalues and Eigenvectors to find the general solution of the following system of differential equations:

y1' = 4y1 + 5y2
y2' = -2y1 + 6y2

Solution:

Write the form of particular Solution with the method of undetermined coefficients.

Write the form of particular Solution with the method of undetermined coefficients.

A) y'' + 6y' + 9y = 5cos(2x)

B) y'' + 10y' + 24y = 3xe^6x

C) y'' - 9y' + 18y = 3e2x + 7x³sin(4x)

Solution:

Convert the initial value problem into a first order system. Give the matrix A which determines the system and the initial vector x(0). y'' - 3y' - 10y = 3e^(-2t) + 2e^(5t) y(0)=2, y'(0)= -3

Convert the initial value problem into a first order system. Give the matrix A which determines the system and the initial vector x(0).

y'' - 3y' - 10y = 3e^-2t + 2e^5t

y(0)=2, y'(0)= -3

Solution: