# Illustration Difference between initial conditions and boundary conditions

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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.