Question

please explain how to see if linear or nonlinear. i dont understand why its both here. thank you!

In each of Problems through 4.verjfy that (0,0) is a critical point, show that the system is locally linear, and discuss the type and stability of the critical point (0...0) by examining the corresponding linear system, 1. dx/dt = x -y dyldt= x - 2y + x? ANSWER lincar and nonlinear saddle point, unstable

Answer 1

x chox to dy - x-2y + H² This is non-linear form. Check at (0,o) is critical point. de fin,y) = x-42 of 3 ke -ay Seg(y) = -2y+* f ) 09 - 1 + Now , Convert into linear. Frais) = fop) + ( + y (of (0,0) 20 ta ty (o) + 9 ( 5 ) ) G (x,y) a glo,p) + ( 2 x (i) + 9 (-2) FGiy) - a toy G (ny) zx - 2y - -

CF(ny) 7 Glny 2, 2 g (Adl=0 1 -2- (1-2) (+) 20 soots are So, point real, unequal and of opposite so cool is saddle point and unstable.
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