1. Two applications are given, to hamiltonian differential systems and to a variant of the wave equation.

2. What is the differential equation?

3. A differential equation is simply an equation that contains a derivate.

4. Let's say this is my differential equation.

5. The calculation method uses partial differential equation.

6. So, for example, this is a differential equation.

7. So how do we solve this differential equation?

8. The swing equation of the machine is a third-order nonlinear differential equation.

9. In a nonlinear geometrical acoustics theory the transport equations which determine the signal carried by a component wave have the form of a simple wave equation, Korteweg-de Vries equation, damped simple wave equation and Burgers' equation.

10. The Galerkin formulation is applied to the differential equation.

11. This kind of relationship is called a differential equation.

12. An ordinary differential equation is what I wrote down.

13. The differential equation must be at least first-order

14. This differential equation is the classic equation of motion of a charged particle in vacuum.

15. So this is the general solution to this differential equation.

16. Film bulk acoustic wave resonator with differential topology

17. So the first question is: what is a differential equation?

18. It is a particular case of the Lagrange differential equation.

19. But I am telling you, an ordinary differential equation supports this.

20. This is a special case of a separable partial differential equation.

21. Resolving a differential equation means finding the functions that satisfy it.

22. That is our simple differential equation that models continuous compounded interest.

23. In mathematics, a (real) Monge–Ampère equation is a nonlinear second-order partial differential equation of special kind.

24. The Hamilton–Jacobi–Bellman (HJB) equation is a partial differential equation which is central to optimal control theory.

25. §15.5(ii) Contiguous Functions Keywords: Contiguous , equivalent equation for Contiguous functions , hypergeometric differential equation , hypergeometric function , recurrence relations

26. This example demonstrates the use of lsode, an ordinary differential equation solver.

27. I'm telling you, the Lenwoloppali Differential Equation Scanner meets a real need.

28. Now, all of the sudden, I have a non- linear differential equation.

29. The attendant one - dimensional wave equation has mesmerizing harmonic properties.

30. The elliptical drumhead was studied by Émile Mathieu, leading to Mathieu's differential equation.

31. The resulting model, in terms of a stochastic differential equation, is solved analytically.

32. Using the group foliation method to solve the nonlinear wave equation.

33. A differential equation is developed and solved, describing this phase of the impact.

34. So once we solve this differential equation, and this is a separable differential equation, then we can use this initial condition, when x is 0, y is 1, to figure out the constant.

35. In Quantum Mechanics, we understand this wave-particle duality using (complex) probability Amplitudes which satisfy a wave equation

36. The solutions of this differential equation have singularities unless λ takes on specific values.

37. Humidity field in the concrete may be found by solving the diffusion differential equation.

38. The consequences of this change are constant coefficients in a linear ordinary differential equation system.

39. The generator potential is to be described by a linear differential equation of second order.

40. And all of you know the wave equation is the frequency times the wavelength of any wave ... is a constant.

41. The steady state is here regarded as the solution of a partial differential-algebraic equation.

42. A more thorough analysis of this inhomogeneous differential equation leads to a modified Hill determinant.

43. A solution to the differential equation may be found by the usual series expansion method.

44. And we know a solution of our original differential equation is psi is equal to c.

45. In most cases, already the linearized form of this differential equation yields solutions of sufficient accuracy.

46. Based on the theory of stochastic differential equation, the physical property of price model was proved.

47. A multispectral bioluminescence optical tomography algorithm makes use of a partial differential equation (PDE) constrained approach.

48. These models are nonlinear system of Conformable fractional differential equation (CFDE) that has no analytic solution.

49. The use of a certain pressure law leads to a partial differential equation for the motion.

50. 15 Higher-order antithetical couplets synchronization of gravity wave equation with the primary soud.

51. The explicit calculation of normal coordinates can be accomplished by considering the differential equation satisfied by geodesics.

52. The description of the theoretical model by an integro-differential equation shows interactions between those three different phenomena.

53. Surface acoustic wave device for a differential phase-shift direct-sequence spread-spectrum signal receiver

54. This nonlinear partial differential equation is resolved by perturbation theory for the particular case of a homogeneous system.

55. It will be represented a general method to derive difference-equation for numerical solution of partial differential-equations.

56. The idea is to replace the derivatives appearing in the differential equation by finite differences that approximate them.

57. Two new three step formulae are introduced for the numerical integration of a first order ordinary differential equation.

58. The differential equation given by Herring for the case of the forced vibrations is completed and solved numerically.

59. In another major paper from this era, Einstein gave a wave equation for de Broglie waves, which Einstein suggested was the Hamilton–Jacobi equation of mechanics.

60. All quantities that influence the wave propagation of radar signals were taken into account at this equation.

61. Control differential equation of curve problem of variable-thickness cylindrical shell is deduced with cell theory of variable-thickness shell.

62. The Advection diffusion equation is the partial differential equation $$\frac{\partial C}{\partial t} = D\frac{\partial^2 C}{\partial x^2} - v \frac{\partial C}{\partial x}$$ with the boundary cond

63. By showing the analogy of Ritz or the extended Galerkin method with the approximation of a certain integro-differential equation, means are obtained for proving the convergence of Ritz or the extended Galerkin method indirectly by proving the convergence of the analoguous approximate integro-differential equation.

64. Because of its relationship to the wave equation, the Helmholtz equation arises in problems in such areas of physics as the study of electromagnetic radiation, seismology, and acoustics.

65. The plane-section assumption was not Congruous in low strain dynamic tests on pipe piles, so the propagation of stress wave couldn't be expressed by 1D wave equation

66. The plane-section assumption was not congruous in low strain dynamic tests on pipe piles, so the propagation of stress wave couldn't be expressed by 1D wave equation.

67. GNU MCSim is a simulation and statistical inference tool for algebraic or differential equation systems, optimized for performing Monte Carlo analysis.

68. The method of undetermined coefficients is the general method of solving a linear differential equation with constant coefficients of the second order.

69. The non self-adjoint differential equation and boundary conditions are considered to have random field coefficients. The standard perturbation method is employed.

70. 30 Through the analysis of this wave equation, we find there exists the skin effect in the superconductor, of which the skin depth is dependent on the wave frequency.

71. So we verified that for this function, for y1 is equal to e to the minus 3x, it satisfies this differential equation.

72. 1926 Erwin Schrödinger proposes the Schrödinger equation, which provides a mathematical basis for the wave model of atomic structure.

73. So the general solution to this differential equation is y squared over 2 minus x squared over 2 is equal to c.

74. An algorithm is developed, analogous to a partial differential equation of first order, to describe elements of the path of every contact point.

75. So using these conditions, a point where this function crosses through, we can now give you the particular solution to this differential equation.

76. But anyway, I've run out of time, and hopefully that gives you a good at least survey of what a differential equation is.

77. The Schrödinger equation describes how wave functions change in time, playing a role similar to Newton's second law in classical mechanics.

78. The bending moment at this section = Pcr.y The differential equation governing the small Buckling deformation is given by P y dx d y EI cr

79. 1 Anharmonic oscillator is an oscillator (i.e. a physical system that exhibits a periodic motion), which is not described by a linear differential equation (i.e

80. The main feature of this technique is that the original boundary value problem associated with the differential equation is reduced to an algebraic eigenvalue problem.