(c) (10%) Draw the phase plane portraits for the solutions (x₁,x₂) of the following initial conditions:(x₁₀,x₂₀)=(0,0.5),(-1,0), and (1,-1).

(a) (15%) Let u(t) = O and the initial conditions bex1(0)=x2(0)=1,.Find the solutions of the differential equations.

(b) (5%) Let initial conditions be x1(0)=x2(0)==0, and u(t) be the unit step function. Does the solutions of the differential equations converge to constant values as time approaches infinity? Justify your answers.

(a) (10%) Express the differential equations using the polar coordinate； i.e. express the equations in terms of (r, θ), where x1(t) =r(t) cos(θ(t)) and x2(t) =r(t) sin(θ(t).

(b) (10%) Solve the differential equations for any nonzero initial conditions (x10, x20).

(c) (5%) Suppose A = B+iC is a Hermitian matrix and let . Show that any eigenvalue λ of Ω is also an eigenvalue of A . 

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