Internal problem ID [2447]
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: 14.
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^{2}+6\right ) y^{\prime }+6 y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 33
Order:=6; dsolve(x^2*diff(y(x),x$2)+x*(6+x^2)*diff(y(x),x)+6*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \frac {c_{1} \left (1+\frac {1}{3} x^{2}+\mathrm {O}\left (x^{6}\right )\right ) x +c_{2} \left (1+\frac {3}{2} x^{2}+\frac {1}{8} x^{4}+\mathrm {O}\left (x^{6}\right )\right )}{x^{3}} \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 33
AsymptoticDSolveValue[x^2*y''[x]+x*(6+x^2)*y'[x]+6*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {1}{x^3}+\frac {x}{8}+\frac {3}{2 x}\right )+c_2 \left (\frac {1}{x^2}+\frac {1}{3}\right ) \]