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- https://math.libretexts.org/Courses/Coastline_College/Math_C285%3A_Linear_Algebra_and_Diffrential_Equations_(Tran)/15%3A_Fourier_series_and_PDEs/15.01%3A_Boundary_value_problemsBefore we tackle the Fourier series, we need to study the so-called boundary value problems (or endpoint problems).
- https://math.libretexts.org/Bookshelves/Differential_Equations/Introduction_to_Partial_Differential_Equations_(Herman)/02%3A_Second_Order_Partial_Differential_Equations/2.03%3A_Boundary_Value_ProblemsFor an initial value problem one has to solve a differential equation subject to conditions on the unknown function and its derivatives at one value of the independent variable. Typically, initial val...For an initial value problem one has to solve a differential equation subject to conditions on the unknown function and its derivatives at one value of the independent variable. Typically, initial value problems involve time dependent functions and boundary value problems are spatial. With an initial value problem one knows how a system evolves in terms of the differential equation and the state of the system at some fixed time; one seeks to determine the state of the system at a later time.
- https://math.libretexts.org/Courses/Lake_Tahoe_Community_College/MAT-204%3A_Differential_Equations_for_Science_(Lebl_and_Trench)/06%3A_Fourier_series_and_PDEs/6.01%3A_Boundary_value_problemsBefore we tackle the Fourier series, we need to study the so-called boundary value problems (or endpoint problems).
- https://math.libretexts.org/Bookshelves/Differential_Equations/Elementary_Differential_Equations_with_Boundary_Value_Problems_(Trench)/13%3A_Boundary_Value_Problems_for_Second_Order_Linear_Equations/13.01%3A_Boundary_Value_ProblemsThis section discusses point two-point boundary value problems for linear second order ordinary differential equations.
- https://math.libretexts.org/Bookshelves/Differential_Equations/Differential_Equations_for_Engineers_(Lebl)/4%3A_Fourier_series_and_PDEs/4.01%3A_Boundary_value_problemsBefore we tackle the Fourier series, we need to study the so-called boundary value problems (or endpoint problems).
- https://math.libretexts.org/Bookshelves/Applied_Mathematics/Numerical_Methods_(Chasnov)/07%3A_Ordinary_Differential_Equations/7.01%3A_Examples_of_Analytical_SolutionsThe differential equation (7.1) is separable, and separating and integrating from time \(t=0\) to \(t\) yields \[\int_{q_{0}}^{q} \frac{d q}{q}=-\frac{1}{R C} \int_{0}^{t} d t \nonumber \] which can b...The differential equation (7.1) is separable, and separating and integrating from time \(t=0\) to \(t\) yields \[\int_{q_{0}}^{q} \frac{d q}{q}=-\frac{1}{R C} \int_{0}^{t} d t \nonumber \] which can be integrated and solved for \(q=q(t)\) : \[q(t)=q_{0} e^{-t / R C} . \nonumber \] The classic second-order initial value problem is the \(R L C\) circuit, with differential equation \[L \frac{d^{2} q}{d t^{2}}+R \frac{d q}{d t}+\frac{q}{C}=0 . \nonumber \] Here, a charged capacitor is connected to …
