Label the following statements as true or false.{a) The set of solut ions to an nth-order homogeneous linear differentialequation with constant coefficients is an n-dimensional subspace ofcoo. (b) The solution space of a homogeneous linear differential equationwith constant coefficients is the null space of a differential operator.(c) The auxiliary polynomial of a homogeneous linear differentialequation with constant coefficients is a solution to the differentialequation.(d) Any solution to a homogeneous linear different ial equation withconst ant coefficients is of the form aect or atkect , where a and care complex numbers and k is a positive integer. (e) Any linear combination of solutions to a given homogeneous lineardifferential equation with constant coefficients is also a solution tothe given equation.
Label the following statements as true or false.
{a) The set of solut ions to an nth-order homogeneous linear
equation with constant coefficients is an n-dimensional subspace of
coo. (b) The solution space of a homogeneous linear differential equation
with constant coefficients is the null space of a differential operator.
(c) The auxiliary polynomial of a homogeneous linear differential
equation with constant coefficients is a solution to the differential
equation.
(d) Any solution to a homogeneous linear different ial equation with
const ant coefficients is of the form aect or atkect , where a and c
are
(e) Any linear combination of solutions to a given homogeneous linear
differential equation with constant coefficients is also a solution to
the given equation.
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