Internal problem ID [2454]
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: 21.
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 (3 x +2\right ) y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.017 (sec). Leaf size: 65
Order:=6; dsolve(x^2*diff(y(x),x$2)-x^2*diff(y(x),x)-(3*x+2)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \frac {c_{1} x^{3} \left (1+\frac {5}{4} x +\frac {3}{4} x^{2}+\frac {7}{24} x^{3}+\frac {1}{12} x^{4}+\frac {3}{160} x^{5}+\mathrm {O}\left (x^{6}\right )\right )+c_{2} \left (\ln \relax (x ) \left (24 x^{3}+30 x^{4}+18 x^{5}+\mathrm {O}\left (x^{6}\right )\right )+\left (12-12 x +18 x^{2}+26 x^{3}+x^{4}-9 x^{5}+\mathrm {O}\left (x^{6}\right )\right )\right )}{x} \]
✓ Solution by Mathematica
Time used: 0.023 (sec). Leaf size: 84
AsymptoticDSolveValue[x^2*y''[x]-x^2*y'[x]-(3*x+2)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {1}{2} x^2 (5 x+4) \log (x)-\frac {3 x^4-6 x^3-6 x^2+4 x-4}{4 x}\right )+c_2 \left (\frac {x^6}{12}+\frac {7 x^5}{24}+\frac {3 x^4}{4}+\frac {5 x^3}{4}+x^2\right ) \]