Find all real-valued solutions to the following differential equation: 16x(5)(t)+8π2x′′′(t)+π4x′(t)=0. (a) Now, find all

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Find all real-valued solutions to the following differential equation: 16x(5)(t)+8π2x′′′(t)+π4x′(t)=0. (a) Now, find all (real-valued) solutions that satisfy the initial conditions at t=1 : x(1)=1,x′(1)=2π​. (b) Find all (real-valued) solutions satisfying the following initial conditions: x(k)(1)=(2π​)k(cos(2πk​)+sin(2πk​)),k∈{0,1,…,4}.