Question

Problem 2. S x' = 5x – 4y (8 points) Find the solution to the linear system of differential equations I y' = 2x – y satisfying the initial conditions x(0) = 3 and y(0) = 2. e(t) = g(t) = Note: You can earn partial credit on this problem. preview answers

Answer 1

sx 50 yy no)- 3 ly's any ay (6)=2 Let a = D. Da - 5x+4y co - - y - 2x + y = 0 0-5)+ yy 0 -2x + 6tly to - - (2) Multiply by (0-5) in by 2 in equation (1) . me get [CD+/260-5) +8] y = 0 (D²-4D 13.) y co Auxxliary equation. e²-Ye +3 =0 r² #3r-r+3=0 ele-3) -11e-3) 20 e-3) (e-) )=0 =) e=3 and eal >) y(t)- Gest't caet y(0)=2 - C1:+C2=d

Putting value of y in equation (2 :-20 + (D+1) (cieltº+Cgét)0 - 27 + 3cielt toettcreteceet = 0 .-2x + 40,0 ²t +acet=0 -2x = - uciet zozet x= acie?t +caeb. Лоо ке ) = 3 = 2017 C2 = 3 So, me have 24+ (x=3 and ci + C2 = 2 → Ci - 1+ C2 = 2 =>C2=1 So y(t)= ettet. and alt) = delt + eti