Consider the system of linear differential equations (t)2/51 (t) 11/5 z2(t) /5()+17/52 (t) We want to determine the stability of the origin 1 (t) 22 (t) a) This system can be written in the form X' = AX, where x(t) = bsin a) or b) Find the eigenvalues of A. List them between square braquets and separated by commas Eigenvalues c) From (b), we can conclude that the origin is stable asymptotically stable unstable
because one of the eigenvalues is zero at least one of the eigenvalues is positive. both eigenvalues are negative
Show transcribed image text Consider the system of linear differential equations (t)2/51 (t) 11/5 z2(t) /5()+17/52 (t) We want to determine the stability of the origin 1 (t) 22 (t) a) This system can be written in the form X' = AX, where x(t) = bsin a) or b) Find the eigenvalues of A. List them between square braquets and separated by commas Eigenvalues c) From (b), we can conclude that the origin is stable asymptotically stable unstable
because one of the eigenvalues is zero at least one of the eigenvalues is positive. both eigenvalues are negative