Internal problem ID [2420]
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: 14.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {3 x^{2} y^{\prime \prime }-x \left (8+x \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: 0.016 (sec). Leaf size: 47
Order:=6; dsolve(3*x^2*diff(y(x),x$2)-x*(x+8)*diff(y(x),x)+6*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = c_{1} x^{\frac {2}{3}} \left (1-\frac {1}{6} x +\frac {5}{36} x^{2}+\frac {5}{81} x^{3}+\frac {11}{972} x^{4}+\frac {77}{58320} x^{5}+\mathrm {O}\left (x^{6}\right )\right )+c_{2} x^{3} \left (1+\frac {3}{10} x +\frac {3}{65} x^{2}+\frac {1}{208} x^{3}+\frac {3}{7904} x^{4}+\frac {21}{869440} x^{5}+\mathrm {O}\left (x^{6}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 88
AsymptoticDSolveValue[3*x^2*y''[x]-x*(x+8)*y'[x]+6*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {21 x^5}{869440}+\frac {3 x^4}{7904}+\frac {x^3}{208}+\frac {3 x^2}{65}+\frac {3 x}{10}+1\right ) x^3+c_2 \left (\frac {77 x^5}{58320}+\frac {11 x^4}{972}+\frac {5 x^3}{81}+\frac {5 x^2}{36}-\frac {x}{6}+1\right ) x^{2/3} \]