Internal problem ID [4758]
Book: Notes on Diffy Qs. Differential Equations for Engineers. By by Jiri Lebl, 2013.
Section: Chapter 7. POWER SERIES METHODS. 7.2.1 Exercises. page 290
Problem number: 7.2.8 part(b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {x y^{\prime \prime }+y=0} \end {gather*} With the expansion point for the power series method at \(x = 1\).
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 49
Order:=6; dsolve(x*diff(y(x),x$2)+y(x)=0,y(x),type='series',x=1);
\[ y \relax (x ) = \left (1-\frac {\left (x -1\right )^{2}}{2}+\frac {\left (x -1\right )^{3}}{6}-\frac {\left (x -1\right )^{4}}{24}+\frac {\left (x -1\right )^{5}}{60}\right ) y \relax (1)+\left (x -1-\frac {\left (x -1\right )^{3}}{6}+\frac {\left (x -1\right )^{4}}{12}-\frac {\left (x -1\right )^{5}}{24}\right ) D\relax (y )\relax (1)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 78
AsymptoticDSolveValue[x*y''[x]+y[x]==0,y[x],{x,1,5}]
\[ y(x)\to c_1 \left (\frac {1}{60} (x-1)^5-\frac {1}{24} (x-1)^4+\frac {1}{6} (x-1)^3-\frac {1}{2} (x-1)^2+1\right )+c_2 \left (-\frac {1}{24} (x-1)^5+\frac {1}{12} (x-1)^4-\frac {1}{6} (x-1)^3+x-1\right ) \]