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Laplace transform is an integral transform employed in solving physical problems. Many physical problems when analyses assumes the form of a differential equation subjected to a set of initial conditions or boundary conditions.
By initial conditions we mean that the conditions on the dependent variable are specified at a single value of the independent variable. If the conditions of the dependent variable are specified at two different values of the independent variable, the conditions are called boundary conditions. The problem with initial conditions is referred to as the Initial value problem. The problem with boundary conditions is referred to as the Boundary value problem.