A second order differential equation 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 in the Taylor polynomial, if one is either given or can solve for the initial condition y(0) and y'(0). What is the coefficient of x⁴ in the Taylor polynomial expansion of the solution to the equation if the initial conditions are ?

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The Answer of A second order differential equation 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 in the Taylor polynomial, if one is either given or can solve for the initial condition y(0) and y'(0). What is the coefficient of x⁴ in the Taylor polynomial expansion of the solution to the equation if the initial conditions are ?

A Second Order Differential Equation Can Be Arranged to the Form