Internal problem ID [2461]
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: 28.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Laguerre, [_2nd_order, _linear, _with_symmetry_[0,F(x)]]]
Solve \begin {gather*} \boxed {x y^{\prime \prime }-y^{\prime } x +y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 42
Order:=6; dsolve(x*diff(y(x),x$2)-x*diff(y(x),x)+y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (-x +\mathrm {O}\left (x^{6}\right )\right ) \ln \relax (x ) c_{2}+c_{1} \left (1+\mathrm {O}\left (x^{6}\right )\right ) x +\left (1+x -\frac {1}{2} x^{2}-\frac {1}{12} x^{3}-\frac {1}{72} x^{4}-\frac {1}{480} x^{5}+\mathrm {O}\left (x^{6}\right )\right ) c_{2} \]
✓ Solution by Mathematica
Time used: 0.025 (sec). Leaf size: 41
AsymptoticDSolveValue[x*y''[x]-x*y'[x]+y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {1}{72} \left (-x^4-6 x^3-36 x^2+144 x+72\right )-x \log (x)\right )+c_2 x \]