Question

Classify the critical point (0, 0) of the given linear system. Draw a phase portrait. dx/df 3x+ y a. dx/dt -x+ 2y dx/dt =-x +3y dy/dt -2x + y dy/dt x+ y Classify the stationary point (0, 0) of the given linear system. Draw a phase portrait. dy/dt -x+y b. dx/dt =-2x-y dx/dt-2x +5/7 y dx/dt 3x-y dx/dt 3x dy/dt 3x- y dy/dt 7x- 3y dy/dt x+y dy/dt 3y

Answer 1

com . Note that is the only equilibrium Point per i liven system *2384 [$]+[:51:3 (54)= X-AX y = -axty nial of A.-B is be of AAA 1241 UULE polynomial chanaderistic d2 Grace) Ald 4 IAI=0 12-47 +5=0 de 4 16-20 e-values . Since Both part 9 (0,0) tve Real are complex is. Unstable with Spiral EÓJ: [1 ] [53: A[14] Cip of - - (trare Did † 1A) = 0 d2..3 #muovios sa real and Bota and real saddle Node e ince of are Both eigen Valves (0,0), is opposite . sign a . ( Unstable ) eto e 0,01 vs saddle

Part 1 033 001 C A E AJ JD3] aceite 22+30 Det si 1 Since Bote evalues are Burely imaginary = (0,0) is centre i e' stabla imaginary .(2) Part -2-7a 1.3 JL Asyptotically Vglable 1 CAP. d2 +32.45 = 0. dz 94 59-20; d. -3 At 0,09 There is STE' 2 cónverginging Spiral. Since Both e-value Son complex numbers Spiral one the 6,01 cís ie Asymptotically Statele Converging