Internal problem ID [2444]
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: 11.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} \left (x +1\right ) y^{\prime \prime }+y^{\prime } x^{2}-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: 39
Order:=6; dsolve(x^2*(1+x)*diff(y(x),x$2)+x^2*diff(y(x),x)-2*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = c_{1} x^{2} \left (1-x +\frac {9}{10} x^{2}-\frac {4}{5} x^{3}+\frac {5}{7} x^{4}-\frac {9}{14} x^{5}+\mathrm {O}\left (x^{6}\right )\right )+\frac {c_{2} \left (12+6 x +\mathrm {O}\left (x^{6}\right )\right )}{x} \]
✓ Solution by Mathematica
Time used: 0.025 (sec). Leaf size: 47
AsymptoticDSolveValue[x^2*(1+x)*y''[x]+x^2*y'[x]-2*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (\frac {5 x^6}{7}-\frac {4 x^5}{5}+\frac {9 x^4}{10}-x^3+x^2\right )+c_1 \left (\frac {1}{x}+\frac {1}{2}\right ) \]