use the elimination method to find the general solution for the
given linear system where differentiation is with respect to t.
2x'+y'-x-2y=e^-t and x'+y'+2x+2y==e^t
Use the elimination method to find a general solution for the
given linear system, where differentiation is with respect to
t.
x'=9x-2y+sin(t)
y'=25x-y-cos(t)
Use the method of eigenvalues and eigenvectors to find the
general solution to the following system of differential
equations.
x′(t) = 2x(t) + 2y(t) − z(t)
y′(t) = 0 + 3y(t) + z(t)
z′(t) = 0 + 5y(t) − z(t)
Use the Gauss-Jordan elimination method to solve the following
system of linear equations. State clearly whether the system has a
unique solution, infinitely many solutions, or no solutions. { ? +
2? = 9
? + ? = 1
3? − 2? = 9
Use the method of Undetermined Coefficients to find a general
solution of this system X=(x,y)^T
Show the details of your work:
x' = 6 y + 9 t
y' = -6 x + 5
Note answer is: x=A cos 4t + B sin 4t +75/36; y=B cos
6t - A sin 6t -15/6 t
Use Cramer's Rule to find the solution of the system of linear
equations, if a unique solution exists.
–5x + 2y – 2z = 26
3x + 5y + z = –22
–3x – 5y – 2z = 21
Find the general solution of the linear system
x ̇1 = x1, x ̇2 = ax2
Where a is a constant. Draw the phase planes for a = −1, 0, 1. Comment on the changes of the phase plane
Use the graphical method for linear programming to find the
optimal solution for the following problem.
Maximize P = 4x + 5 y
subject to 2x + 4y ≤ 12
5x + 2y ≤ 10
and x ≥ 0, y ≥
0.
graph the feasible region