Find the fundamental matrix Ψ(t) satisfying Ψ(0) = I for the system of equations. X'(t) = [-1 -4 ; 1 -1] X(t)

Question.

Find the fundamental matrix Ψ(t) satisfying Ψ(0) = I for the system of equations.

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:

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:

Solve the system of differential equations by systematic elimination. dx/dt = -2x - y ; dy/dt = -4y

Question.

Solve the system of differential equations by systematic elimination.

dx/dt = -2x - y
dy/dt = -4y

Solution:

Find the general solution of the given system of differential equations. dx/dt = - 10x + 8y , dy/dt = - 11x/8 + 2y

Question.

Find the general solution of the given system of differential equations.

dx/dt = - 10x + 8y

dy/dt = - 11x/8 + 2y

Solution:

Find the general solution of the given system using method of Eigenvalues dx/dt = 7x - 4y , dy/dt = x + 2z , dz/dt = 2y + 7z

Question.

Find the general solution of the given system using method of Eigenvalues

dx/dt = 7x - 4y

dy/dt = x + 2z

dz/dt = 2y + 7z

Solution:

x''+3y'+3y=0 , x''+3y=te^-t, x(0)=8 , x'(0)=2 , y(0)=0

Use Laplace transform to solve the system, with the given initial conditions. x''+3y'+3y=0 and x''+3y=te^-t x(0)=8 x'(0)=2 and y(0)=0

x' = -6x - 4y , y' = -3x - 10y

find the general solution of x'=-6x-4y and y'=-3x-10y

x' = y - x + t , y' = y , x(0)=6 , y(0)=8

Find the solution to 

x' = y - x + t
y' = y
if x(0)=6 and y(0)=8

System of Differential equations - 2nd order - undetermined coefficients

System of Differential equations - 2nd order - undetermined coefficients

System of Differential equations - 3rd order - undetermined coefficients