Let x and y be functions of t. Find the general solution of the system of equations below by first converting the system

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Let X And Y Be Functions Of T Find The General Solution Of The System Of Equations Below By First Converting The System 1 (79.35 KiB) Viewed 13 times

Let x and y be functions of t. Find the general solution of the system of equations below by first converting the system into second-order differential equations involving only y and only x. Find a particular solution for the initial conditions. Use a computer system or graphing calculator to construct a direction field and typical solution curves for the given system. x' = 8y, y'= -2x; x(0)=2, y(0) = 2 Solve for x(t). Choose the correct answer below. OA. x(t) = A e 4t +Be-4t OB. x(t) = A cos (8t) + B sin (8t) C. x(t) = A cos (4t) + B sin (4t) O D. x(t)=Ae8t + Be Now find y(t) so that y(t) and the solution for x(t) found in the previous step are a general solution to the system of differential equations. -8t y(t) = B cos (4t)- A sin (4t) C OA Find the particular solution based on the initial values x(0) = 2, y(0) = 2. x(t) = 2 cos (4t) + 4 sin (4t) y(t) = 2 cos (4t) - sin (4t) Use a computer system or graphing calculator to construct a direction field and typical solution curves for the system. Select the correct graph below. OB.