Answer to Question #5983 in Differential Equations for Akhtar Rasoolddd
what is initial value problems and boundary vale problems.
A simple example is to solve y' = 0.85y and y(0) = 19. We are trying to find a formula for y(t) that satisfies these two equations.
A boundary value problem is a differential equation together with a set of additional restraints, called the boundary conditions. A solution to a boundary value problem is a solution to the differential equation which also satisfies the boundary conditions.
Concretely, an example of a boundary value (in one spatial dimension) is the problem
y"(x) + y(x) = 0
to be solved for the unknown function y(x) with the boundary conditions
y(0) = 0, y(pi/2) = 2.
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