Answered: iderivative must be continuous and…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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1. Which of the following is TRUE for a differential equation? (a) To determine that the DE has a unique solution, its antiderivative must be continuous and satisfy the Lipschitz condition for any positive constant Lipschitz L. (b) To determine that the DE has a unique solution, its antiderivative must be continuous and satisfy the Lipschitz condition for any nonnegative constant Lipschitz L. (c) To determine that the DE has a unique solution, its antiderivative must be differentiable and satisfy the Lipschitz condition for any positive con- stant Lipschitz L. (d) To determine that the DE has a unique solution, its antiderivative must be differentiable and satisfy the Lipschitz condition for any nonnegative constant Lipschitz L. (c) The potential function of the ODE must be specified such that it must be given to determine the solutions of the general solutions. (d) The above statements are true if and only if the given equation is an ordinary differential equations. II. Elimination of Arbitrary Constant 1. Which of the following is not the sense of why there is a need for arbitrary constant? (a) to determine the possible potential function of the representation of curves. (b) to determine unique solution of the differential equations. (c) to determine the possible particular solution of the differential equations. (d) to determine the solution representation for generation matrix in deter- mining if the point is stable or not. 2. Which of the following applications can be a goal of eliminating arbitrary constant? (a) determining families of curves (b) checking appropriate domain of solutions 1 Do not distribute (MARK CAAY) DRAFT (c) stability of equilibrium points (d) all of the above

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