Question

Remaining time: 269.39 min (1 point) -98 a. Find the most general real-valued solution to the linear system of differential equations ' = - :: xi () = C1 + C2 x2 (1) b. In the phase plane, this system is best described as a O source / unstable node sink / stable node O saddle O center point / ellipses O spiral source O spiral sink O none of these

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Answer 1

(9) 18 11 8 :: OC -6 5. charateristic potuequation det(A-1I)=0 $]-[:] - 9 8 -6 -D => => 1-g-A 8 - 6 =0 5-1 > (-9-1) (5-1) + 48=0 - 45 + 9 +-5d+d²+48=0 x² + 4x +3=0 x2 + 3x+x+3=0 Alt+3)+1LX+3)=0 > (1+1)(1+3) = 0 d=-1 d=-3 eigen Vecton corresponding to d= -1 (A-AI) X=0 9 8 -6S 3-1))-[:] EN- 1 6

R₂ -8 R₂ -(-6)R, F-8 8 52 - 8x, +8X₂=0 |x, = x2 eigenvecton XER let x,=1 [1] eigen vecton connesponding to 1=-3 (A-AI) X=0 9 -6 $12)] 1] A10] -G 8 8 R₂ R₂ -R, -6 8. 11:0 O -6% = -8% eigenveltor wie san pc,= 4x2

let x₂=1 - 1 X-T%**(4) -3t e Xu cre are real and eigen values are A=-1, d=-3 distinct ( same sign (-ves) Hature of critical point No de Stable