Internal problem ID [2430]
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: Example 11.5.5 page 768.
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 -\left (x +4\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: 61
Order:=6; dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)-(4+x)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \frac {c_{1} x^{4} \left (1+\frac {1}{5} x +\frac {1}{60} x^{2}+\frac {1}{1260} x^{3}+\frac {1}{40320} x^{4}+\frac {1}{1814400} x^{5}+\mathrm {O}\left (x^{6}\right )\right )+c_{2} \left (\ln \relax (x ) \left (x^{4}+\frac {1}{5} x^{5}+\mathrm {O}\left (x^{6}\right )\right )+\left (-144+48 x -12 x^{2}+4 x^{3}-\frac {6}{25} x^{5}+\mathrm {O}\left (x^{6}\right )\right )\right )}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 77
AsymptoticDSolveValue[x^2*y''[x]+x*y'[x]-(4+x)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {x^4-16 x^3+48 x^2-192 x+576}{576 x^2}-\frac {1}{144} x^2 \log (x)\right )+c_2 \left (\frac {x^6}{40320}+\frac {x^5}{1260}+\frac {x^4}{60}+\frac {x^3}{5}+x^2\right ) \]