Internal problem ID [11890]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 6, Series solutions of linear differential equations. Section 6.1. Exercises page
232
Problem number: 7.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x +y x=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 39
Order:=6; dsolve((x^2+1)*diff(y(x),x$2)+x*diff(y(x),x)+x*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \left (1-\frac {1}{6} x^{3}+\frac {3}{40} x^{5}\right ) y \left (0\right )+\left (x -\frac {1}{6} x^{3}-\frac {1}{12} x^{4}+\frac {3}{40} x^{5}\right ) D\left (y \right )\left (0\right )+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 49
AsymptoticDSolveValue[(x^2+1)*y''[x]+x*y'[x]+x*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {3 x^5}{40}-\frac {x^3}{6}+1\right )+c_2 \left (\frac {3 x^5}{40}-\frac {x^4}{12}-\frac {x^3}{6}+x\right ) \]