Internal problem ID [2439]
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: 4.
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 }+y^{\prime } x^{2}-\left (2+x \right ) 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: 47
Order:=6; dsolve(x^2*diff(y(x),x$2)+x^2*diff(y(x),x)-(2+x)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = c_{1} x^{2} \left (1-\frac {1}{4} x +\frac {1}{20} x^{2}-\frac {1}{120} x^{3}+\frac {1}{840} x^{4}-\frac {1}{6720} x^{5}+\mathrm {O}\left (x^{6}\right )\right )+\frac {c_{2} \left (12-12 x +6 x^{2}-2 x^{3}+\frac {1}{2} x^{4}-\frac {1}{10} x^{5}+\mathrm {O}\left (x^{6}\right )\right )}{x} \]
✓ Solution by Mathematica
Time used: 0.025 (sec). Leaf size: 66
AsymptoticDSolveValue[x^2*y''[x]+x^2*y'[x]-(2+x)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {x^3}{24}-\frac {x^2}{6}+\frac {x}{2}+\frac {1}{x}-1\right )+c_2 \left (\frac {x^6}{840}-\frac {x^5}{120}+\frac {x^4}{20}-\frac {x^3}{4}+x^2\right ) \]