Question: Consider the initial value problem (IVP) y??(t)+y(t)=0,y(0)=2,y?(0)=0. (a). [7] Express this IVP as a first-order system of equations of the form x?=Ax,x(0)=a, whereA Ais a22

Consider the initial value problem (IVP)

y??(t)+y(t)=0,y(0)=2,y?(0)=0.

(a). [7] Express this IVP as a first-order system of equations of the form

x?=Ax,x(0)=a,

whereA

Ais a22 anda is a constant vector. Solve the first-order system of equations and confirm your solution by solving the second-order differential equation.

(b). [5] Describe and sketch the direction field and the solution curve for the first-order system of equations in part (a) in the phase plane.

Consider the initial value problem (IVP)y??(t)+y(t)=0,y(0)=2,y?(0)=0.(a). [7] Express this IVP as a

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