Question

Consider the system of differential equations r 10/31+4/322 243+20/822 where c1 and 2 are functions of t. Our goal is first to find the general solution of this system and then a particular solution. a) This system can be written using matrices as X' Ax, where X is in R2 and the matrix A is b sin (a) 7 b) Find the eigenvalues and eigenvectors of the matrix A associated to the system of linear differential equatons. List the eigenvalues separated by semicolons Eigenvalues Give an eigenvector associated to the smallest eigenvalue.

Give an eigenvector associated to the largest eigenvalue. Answer: 00 α Ω 血。 sin (a Oc c) The general solution of the system of linear differential equations is of the orn X c ї с X where c an c are o stants, a d 00 α Ω 0t

and ab sin (a) We assume that X1 is assoicated to the smallest eigenvalue and X2 to the largest eigenvalue. Use the scientific calculator notation. For instance 3e 4t is written d) Find the solution if the initial condition is att 0 Answer: X(t)1 (t) - 2y(0 b sin (a) Ω 血。 00 α

Show transcribed image text Consider the system of differential equations r 10/31+4/322 243+20/822 where c1 and 2 are functions of t. Our goal is first to find the general solution of this system and then a particular solution. a) This system can be written using matrices as X' Ax, where X is in R2 and the matrix A is b sin (a) 7 b) Find the eigenvalues and eigenvectors of the matrix A associated to the system of linear differential equatons. List the eigenvalues separated by semicolons Eigenvalues Give an eigenvector associated to the smallest eigenvalue.
Give an eigenvector associated to the largest eigenvalue. Answer: 00 α Ω 血。 sin (a Oc c) The general solution of the system of linear differential equations is of the orn X c ї с X where c an c are o stants, a d 00 α Ω 0t
and ab sin (a) We assume that X1 is assoicated to the smallest eigenvalue and X2 to the largest eigenvalue. Use the scientific calculator notation. For instance 3e 4t is written d) Find the solution if the initial condition is att 0 Answer: X(t)1 (t) - 2y(0 b sin (a) Ω 血。 00 α