A second order differential equaiton can be arranged to the form , and one can find the third and higher derivatives of y by simply differentiating this equation. Since a Taylor series expansion of a function y(x) is , one can differentiate the rearranged second order differential equation to evaluate coefficients of the Taylor polynomial, if one is either given or can solve for the initial condition y(0) and y'(0). What does the fourth-degree Taylor polynomial look like for the solution to the equation if the initial conditions are ?

Question

A second order differential equaiton can be arranged to the form  , and one can find the third and higher derivatives of y by simply differentiating this equation. Since a Taylor series expansion of a function y(x) is  , one can differentiate the rearranged second order differential equation to evaluate coefficients of the Taylor polynomial, if one is either given or can solve for the initial condition y(0) and y'(0). What does the fourth-degree Taylor polynomial look like for the solution to the equation  if the initial conditions are  ?

Quizplus · Accepted Answer

The Answer of A second order differential equaiton can be arranged to the form  , and one can find the third and higher derivatives of y by simply differentiating this equation. Since a Taylor series expansion of a function y(x) is  , one can differentiate the rearranged second order differential equation to evaluate coefficients of the Taylor polynomial, if one is either given or can solve for the initial condition y(0) and y'(0). What does the fourth-degree Taylor polynomial look like for the solution to the equation  if the initial conditions are  ?

A Second Order Differential Equaiton Can Be Arranged to the Form