Internal problem ID [11887]
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: 4.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+y^{\prime } x +\left (x^{2}-4\right ) y=0} \] 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)+x*diff(y(x),x)+(x^2-4)*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \left (1+2 x^{2}+\frac {1}{4} x^{4}\right ) y \left (0\right )+\left (x +\frac {1}{2} x^{3}-\frac {1}{40} x^{5}\right ) D\left (y \right )\left (0\right )+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 40
AsymptoticDSolveValue[y''[x]+x*y'[x]+(x^2-4)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (-\frac {x^5}{40}+\frac {x^3}{2}+x\right )+c_1 \left (\frac {x^4}{4}+2 x^2+1\right ) \]