Internal problem ID [2414]
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 11.4. page
758
Problem number: 8.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {4 x y^{\prime \prime }-y^{\prime } x +2 y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.014 (sec). Leaf size: 46
Order:=6; dsolve(4*x*diff(y(x),x$2)-x*diff(y(x),x)+2*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \ln \relax (x ) \left (-\frac {1}{2} x +\frac {1}{16} x^{2}+\mathrm {O}\left (x^{6}\right )\right ) c_{2}+c_{1} x \left (1-\frac {1}{8} x +\mathrm {O}\left (x^{6}\right )\right )+\left (1+\frac {1}{4} x -\frac {3}{16} x^{2}+\frac {1}{384} x^{3}+\frac {1}{18432} x^{4}+\frac {1}{737280} x^{5}+\mathrm {O}\left (x^{6}\right )\right ) c_{2} \]
✓ Solution by Mathematica
Time used: 0.025 (sec). Leaf size: 52
AsymptoticDSolveValue[4*x*y''[x]-x*y'[x]+2*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (x-\frac {x^2}{8}\right )+c_1 \left (\frac {x^4+48 x^3-4608 x^2+13824 x+18432}{18432}+\frac {1}{16} (x-8) x \log (x)\right ) \]