Internal problem ID [4513]
Book: Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson
2018.
Section: Chapter 8, Series solutions of differential equations. Section 8.4. page 449
Problem number: 3.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {\left (x^{2}+x +1\right ) y^{\prime \prime }-3 y=0} \end {gather*} With the expansion point for the power series method at \(x = 1\).
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 49
Order:=6; dsolve((1+x+x^2)*diff(y(x),x$2)-3*y(x)=0,y(x),type='series',x=1);
\[ y \relax (x ) = \left (1+\frac {\left (x -1\right )^{2}}{2}-\frac {\left (x -1\right )^{3}}{6}+\frac {7 \left (x -1\right )^{4}}{72}-\frac {\left (x -1\right )^{5}}{20}\right ) y \relax (1)+\left (x -1+\frac {\left (x -1\right )^{3}}{6}-\frac {\left (x -1\right )^{4}}{12}+\frac {\left (x -1\right )^{5}}{24}\right ) D\relax (y )\relax (1)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 78
AsymptoticDSolveValue[(1+x+x^2)*y''[x]-3*y[x]==0,y[x],{x,1,5}]
\[ y(x)\to c_1 \left (-\frac {1}{20} (x-1)^5+\frac {7}{72} (x-1)^4-\frac {1}{6} (x-1)^3+\frac {1}{2} (x-1)^2+1\right )+c_2 \left (\frac {1}{24} (x-1)^5-\frac {1}{12} (x-1)^4+\frac {1}{6} (x-1)^3+x-1\right ) \]