Internal problem ID [2452]
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: 19.
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 (x +3\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: 0.032 (sec). Leaf size: 69
Order:=6; dsolve(x^2*diff(y(x),x$2)-x*(x+3)*diff(y(x),x)+4*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (\left (c_{2} \ln \relax (x )+c_{1}\right ) \left (1+2 x +\frac {3}{2} x^{2}+\frac {2}{3} x^{3}+\frac {5}{24} x^{4}+\frac {1}{20} x^{5}+\mathrm {O}\left (x^{6}\right )\right )+\left (\left (-3\right ) x -\frac {13}{4} x^{2}-\frac {31}{18} x^{3}-\frac {173}{288} x^{4}-\frac {187}{1200} x^{5}+\mathrm {O}\left (x^{6}\right )\right ) c_{2}\right ) x^{2} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 122
AsymptoticDSolveValue[x^2*y''[x]-x*(x+3)*y'[x]+4*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {x^5}{20}+\frac {5 x^4}{24}+\frac {2 x^3}{3}+\frac {3 x^2}{2}+2 x+1\right ) x^2+c_2 \left (\left (-\frac {187 x^5}{1200}-\frac {173 x^4}{288}-\frac {31 x^3}{18}-\frac {13 x^2}{4}-3 x\right ) x^2+\left (\frac {x^5}{20}+\frac {5 x^4}{24}+\frac {2 x^3}{3}+\frac {3 x^2}{2}+2 x+1\right ) x^2 \log (x)\right ) \]