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- Dg 118. Calculus on Manifolds by Michael Spivak, Section 4. Integration of Chains, page 75The characteristic equation for a 5th degree, homogeneous, constant coefficient DE is p(x)=x^3(x^2+1). Which linearly independent functions will be used to form the general solution? A. 1,x,x^2,cos(x),sin(x) B. 1,e^{-x},xe^{-x}, cos(x),sin(x) C. x,x^2,x^3,cos(x),sin(x) D. 1,e^x,xe^x, cos(x),sin(x)True or False The following systemdx/dt = − cos x sin ydy/dt = 2x^2 + sin x cos yis a Hamiltonian system.