Internal problem ID [714]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 5.2, Series Solutions Near an Ordinary Point, Part I. page 263
Problem number: 5.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {\left (1-x \right ) y^{\prime \prime }+y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 49
Order:=6; dsolve((1-x)*diff(y(x),x$2)+y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (1-\frac {1}{2} x^{2}-\frac {1}{6} x^{3}-\frac {1}{24} x^{4}-\frac {1}{60} x^{5}\right ) y \relax (0)+\left (x -\frac {1}{6} x^{3}-\frac {1}{12} x^{4}-\frac {1}{24} x^{5}\right ) D\relax (y )\relax (0)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 63
AsymptoticDSolveValue[(1-x)*y''[x]+y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (-\frac {x^5}{24}-\frac {x^4}{12}-\frac {x^3}{6}+x\right )+c_1 \left (-\frac {x^5}{60}-\frac {x^4}{24}-\frac {x^3}{6}-\frac {x^2}{2}+1\right ) \]