Question

Problem 6. (1 point) Find the most general real-valued solution to the linear system of differential equations & x (1) + C2

Answer 1

x =Ax > x = -4 Step - Determine eigen values [A-I = -z- -4-1 1 + (2 + x +(4+0) (-1) = 0 8 + ² + 6dt i=0 d2+6dt a=0 * (+3)2 = 0 i=-3

This is the case will be of repeated eigenvalues. Solution V2 r(t) = C, et , + c(textu, tentu v eiginnector Ve is solution of (A-d I) v = ve Step 2 » Find eige nuector (A-dI)v=0 [-] xi xz x+2=0 » X₂-- [-] Step 3: Find U₂ - [. 1 y + y2 = 1 Je = ty, 1 ] ty, ]

[i Solution ce Ite x(t) = e 3t