Find the general solution of given system Xmatrixx xtc1c2e3t

Find the general solution of given system. X\'=(matrix)x x(t)=c_1+c_2e^3t+c_3[t+]e^3.

Solution

1) magnitude =[(-43)²+(-4)²]

magnitude =[48+16]

magnitude =64

magnitude =8

direction angle =+tan^-1(4/(43))

direction angle =+tan^-1(1/3)

direction angle =+(/6)

direction angle =7/6

2)let sum =s

fierst term a =1/2, commonratio r =(-1/4/(1/2) =-1/2

sum of infinate series =a/(1-r)

sum =(1/2)/(1-(-1/2))

sum =(1/2)/(3/2)

sum =1/3