## Calculus: Early Transcendentals 8th Edition

(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.