#### Answer

See the work below.

#### Work Step by Step

(a) An initial-value problem consists of finding a solution $y$ of a second-order differential equation that also satisfies the given conditions
$$
y\left(x_{0}\right)=y_{0}
$$
and
$$
y^{\prime}\left(x_{0}\right)=y_{1}
$$
where, $y_{0}$ and $ y_{1} $ are constants.
(b) A boundary-value problem consists of finding a solution $ y$ of a second-order differential equation that also satisfies the given boundary conditions
$$
y\left(x_{0}\right)=y_{0}
$$
and
$$
y\left(x_{1}\right)=y_{1},
$$
where, $y_{0}$ and $ y_{1} $ are constants.