Internal problem ID [405]
Book: Differential equations and linear algebra, 4th ed., Edwards and Penney
Section: Chapter 11 Power series methods. Section 11.1 Introduction and Review of power series. Page
615
Problem number: problem 14.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+y-x=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 38
Order:=6; dsolve(diff(y(x),x$2)+y(x)=x,y(x),type='series',x=0);
\[ y \relax (x ) = \left (1-\frac {1}{2} x^{2}+\frac {1}{24} x^{4}\right ) y \relax (0)+\left (x -\frac {1}{6} x^{3}+\frac {1}{120} x^{5}\right ) D\relax (y )\relax (0)+\frac {x^{3}}{6}-\frac {x^{5}}{120}+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.033 (sec). Leaf size: 56
AsymptoticDSolveValue[y''[x]+y[x]==x,y[x],{x,0,5}]
\[ y(x)\to -\frac {x^5}{120}+\frac {x^3}{6}+c_2 \left (\frac {x^5}{120}-\frac {x^3}{6}+x\right )+c_1 \left (\frac {x^4}{24}-\frac {x^2}{2}+1\right ) \]