Internal problem ID [2453]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 11, Series Solutions to Linear Differential Equations. Exercises for 11.5. page
771
Problem number: 20.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }-y^{\prime } x^{2}-2 y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 45
Order:=6; dsolve(x^2*diff(y(x),x$2)-x^2*diff(y(x),x)-2*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = c_{1} x^{2} \left (1+\frac {1}{2} x +\frac {3}{20} x^{2}+\frac {1}{30} x^{3}+\frac {1}{168} x^{4}+\frac {1}{1120} x^{5}+\mathrm {O}\left (x^{6}\right )\right )+\frac {c_{2} \left (12+6 x -x^{3}-\frac {1}{2} x^{4}-\frac {3}{20} x^{5}+\mathrm {O}\left (x^{6}\right )\right )}{x} \]
✓ Solution by Mathematica
Time used: 0.023 (sec). Leaf size: 63
AsymptoticDSolveValue[x^2*y''[x]-x^2*y'[x]-2*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (-\frac {x^3}{24}-\frac {x^2}{12}+\frac {1}{x}+\frac {1}{2}\right )+c_2 \left (\frac {x^6}{168}+\frac {x^5}{30}+\frac {3 x^4}{20}+\frac {x^3}{2}+x^2\right ) \]