Internal problem ID [2455]
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: 22.
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 }+x \left (5-x \right ) y^{\prime }+4 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: 57
Order:=6; dsolve(x^2*diff(y(x),x$2)+x*(5-x)*diff(y(x),x)+4*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \frac {\left (c_{2} \ln \relax (x )+c_{1}\right ) \left (1-2 x +\frac {1}{2} x^{2}+\mathrm {O}\left (x^{6}\right )\right )+\left (5 x -\frac {9}{4} x^{2}+\frac {1}{18} x^{3}+\frac {1}{288} x^{4}+\frac {1}{3600} x^{5}+\mathrm {O}\left (x^{6}\right )\right ) c_{2}}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 80
AsymptoticDSolveValue[x^2*y''[x]+x*(5-x)*y'[x]+4*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to \frac {c_1 \left (\frac {x^2}{2}-2 x+1\right )}{x^2}+c_2 \left (\frac {\left (\frac {x^2}{2}-2 x+1\right ) \log (x)}{x^2}+\frac {\frac {x^5}{3600}+\frac {x^4}{288}+\frac {x^3}{18}-\frac {9 x^2}{4}+5 x}{x^2}\right ) \]