Internal problem ID [5270]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 3. Linear equations with variable coefficients. Page 130
Problem number: 1(e).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 34
Order:=6; dsolve(diff(y(x),x$2)+y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (1-\frac {1}{2} x^{2}+\frac {1}{24} x^{4}\right ) y \relax (0)+\left (x -\frac {1}{6} x^{3}+\frac {1}{120} x^{5}\right ) D\relax (y )\relax (0)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 42
AsymptoticDSolveValue[y''[x]+y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (\frac {x^5}{120}-\frac {x^3}{6}+x\right )+c_1 \left (\frac {x^4}{24}-\frac {x^2}{2}+1\right ) \]