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The bigest difficulties in the proofs of necessary conditions of the first order for problems in the calculus of variations are caused by a differential equation appearing in the constraints. The right hand side of this equation depends on control, so its maximal solution depends on it too, not only on the initial conditions. We prove that the domain of the maximal solution is an open set, that it has continuous partial derivatives in all variables, and we find its partial derivatives. Using maximal solution of the differential equation, we transform the general problem of the calculus of variations into a smooth problem of mathematical programming. Applying the corresponding necessary conditions of the first order, we obtain the necessary conditions of the first order for the general problem of the calculus of variations