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Initial conditions and boundary conditions sketched for a searched function \(y(t)\):
- Initial conditions - for the function value of the searched function \( y(0) = 1 \) and the derivative of this function \( y'(0) = 1 \) at time \(t = 0\). The initial conditions are constraints at a single point, here \(t = 0 \). Usually the point is at the beginning, hence INITIAL conditions.
- Boundary conditions - for the function value of the searched function \( y(0) = 1 \) at time \(t = 0\) and for the function value of the searched function \( y(6) = 1 \) at another time \( t = 6 \). The boundary conditions are constraints at different points, here at \(t = 0 \) and at \(t = 6\). Usually these points are at the boundaries, hence BOUNDARY conditions.