Lecture 16 - Second order nonhomogeneous linear differential equations: Method of Undetermined Coefficients

ثبت نشده
چکیده

In this lecture we learn to solve nonhomogeneous equations of the form ay′′ + by′ + cy = g(t) using the “method of undetermined coefficients”. In previous lectures we learned to how to solve any equation of the form ay′′ + by′ + cy = 0. We will apply these techniques to help us solve the nonhomogeneous equation ay′′ + by′ + cy = g(t) by understanding the connection between solutions to homogeneous and nonhomogeneous equations.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Solving high-order partial differential equations in unbounded domains by means of double exponential second kind Chebyshev approximation

In this paper, a collocation method for solving high-order linear partial differential equations (PDEs) with variable coefficients under more general form of conditions is presented. This method is based on the approximation of the truncated double exponential second kind Chebyshev (ESC) series. The definition of the partial derivative is presented and derived as new operational matrices of der...

متن کامل

Numerical solution of second-order stochastic differential equations with Gaussian random parameters

In this paper, we present the numerical solution of ordinary differential equations (or SDEs), from each order especially second-order with time-varying and Gaussian random coefficients. We indicate a complete analysis for second-order equations in special case of scalar linear second-order equations (damped harmonic oscillators with additive or multiplicative noises). Making stochastic differe...

متن کامل

An Efficient Numerical Algorithm For Solving Linear Differential Equations of Arbitrary Order And Coefficients

Referring to one of the recent works of the authors, presented in~cite{differentialbpf}, for numerical solution of linear differential equations, an alternative scheme is proposed in this article to considerably improve the accuracy and efficiency. For this purpose, triangular functions as a set of orthogonal functions are used. By using a special representation of the vector forms of triangula...

متن کامل

Iterated Order of Solutions of Certain Linear Differential Equations with Entire Coefficients

In this paper, we investigate the iterated order of solutions of homogeneous and nonhomogeneous linear differential equations where the coefficients are entire functions and satisfy certain growth conditions.

متن کامل

Complex Oscillation of Entire Solutions of Higher-order Linear Differential Equations

In this paper, we investigate higher-order linear differential equations with entire coefficients of iterated order. We improve and extend a result of Beläıdi and Hamouda by using the estimates for the logarithmic derivative of a transcendental meromorphic function due to Gundersen and the WinmanValiron theory. We also consider the nonhomogeneous linear differential equations by using the basic...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2010