day dy For the differential equation + 2 + 37y = 0 dt2 dt (a) Find two different solutions of the form y=e", where r is

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Day Dy For The Differential Equation 2 37y 0 Dt2 Dt A Find Two Different Solutions Of The Form Y E Where R Is 1 (74.06 KiB) Viewed 26 times

day dy For the differential equation + 2 + 37y = 0 dt2 dt (a) Find two different solutions of the form y=e", where r is a complex number constant. (b) Use part (a) to find two real-valued solutions of the differential equation which are not constant multiples of each other. (c) Plot your two solutions of part (b) in the phase plane, and show with an arrow the direction along the curve as t increases. (you might use a computer to help visualize the phase plane curve of the solution of part (b)) (d) Calculate the Wronskian of your two different solutions of part (b), and show that it is not equal to zero. (e) Write down the general solution of this differential equation using the functions of part (b) = (f) Find the solution to this differential equation with initial conditions y(0) = 1 and y'(0) = ( using the functions of part (b).