Question

1. Find the general solution to dr dt = x + 3y dy dt = 4.0 + 2y

Answer 1

x+34 doc dt dy 4x+y dh X'=AX 1 Malo 4 2-1 42 la-lil=O=> 11-13 -> (1-1)(2-1)-19 =0 => 1231-10-0 => t,=5, 12=-2 [9-51] x = -43 4-3 H

X= 3/4 let y=4 V= ༡ 4 d=a [+QI]x=0 4 4 X=-4 2] [3] Fil V= 5L 3 XCE] = Cie 4. 5L :: occt) = 35e 5€ YCE) 4 cie -at ge -2t ta
here we find eigenvalues and eigenvectors of A.

using this we find solution.

x(t) and y(t) is the required solution.