Using matrix algebra, find a general solution to the following system of equations:
x' = 3x - 4y
y' = 4x - 7y
The general solution functions are: ( use c1 and c2 as the constants and enter the elements of the eigenvectors as the lowest integer values. If one element of an eigenvector has a negative value enter the first element as negative.)
x =
y =
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Using matrix algebra, find a general solution to the following system of equations x' = 3x - 4y and y' = 4x - 7y
Find the general solution to the system of linear differential equations X'=AX. The independent variable is t. The eigenvalues and the corresponding eigenvectors are provided for you. x1' = 12x1 - 8x2 x2 = -4X1 + 8x2 The eigenvalues are 11 = 16 and 12 = 4 . The corresponding eigenvectors are: K1 = K2= Step 1. Find the nonsingular matrix P that diagonalizes A, and find the diagonal matrix D: p = 11 Step 2. Find the general solution...
1 point) (a) Find the general solution to y" +7y'-0. Give your answer as y -.. . In your answer, use ci and c2 to denote arbitrary constants and x the independent variable. Enter ci as c1 and c as c2 help (equations) (b) Find the particular solution that satisfies y(0) 1 and y'(0)1 help (equations)
Using matrix algebra, find a general solution to the following system of equations:
3. Solve the system of equations: (-x - 7y = 14 1-4X – 14y = 28 4. Solve the system of equations: 3x - 2y = 2 (5x - 5y = 10 5. Solve the system of equations: (2x + 8y = 6 1-x - 4y = -3
(3 points) (a) Find the general solution to y′′+2y′=0. Give your answer as y=... . In your answer, use c1 and c2 to denote arbitrary constants and x the independent variable. Enter c1 as c1 and c2 as c2. (3 points) (a) Find the general solution to y" + 2y' = 0. Give your answer as y=... . In your answer, use c1 and c2 to denote arbitrary constants and x the independent variable. Enter cı as c1 and C2...
The answer above is NOT correct. (1 point) Find the general solution to y(4) – 8y"" + 15y" = 0. In your answer, use C1,C2,C3 and C4 to denote arbitrary constants and x the independent variable. Enter ci as c1, c2 as c2, etc. y=c1+xc1+c3e^(3x)+c4e^(5x) help (equations)
3. Write the following systems of linear equations using augmented matrix form a. 6x+7y= -9 X-y= 5 b. 2x-5y= 4 4x+3y= 5 C. x+y+z= 4 2x-y-z= 2 -x+2y+3z= 5 4. Solve the following Systems of linear equations using Cramer's Rule a. 6x-3y=-3 8x-4y= -4 b. 2x-5y= -4 4x+3y= 5 c. 2x-3y+z= 5 X+2y+z= -3 x-3y+2z= 1
Solve the system of linear equations using the elimination method x 4y z 18 3x y 4z 9 x 4y 4z 15 - + The unique solution to the system is (Type an exact answer in simplified form.)
Assignment 9: Problem 1 Previous Problem List Next (1 point) Find the general solution to y(4) - 7y" + 12y" = 0. In your answer, use C1, C2, C3 and C4 to denote arbitrary constants and r the independent variable. Enter C as C1, C2 as c2, etc. help (equations)
x'-y,y 10x-7y using the method of elimination. 2) a) Find the general solution to b) What happens to all solutions as ? You should find that all solutions approach the same point (x, y). This is an example of a fixed point. c) Find the particular solution to the IVP consisting of the above system of equations and the conditions x(0)2, y(0)-7