Internal problem ID [2442]
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: 7.
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^{3}-\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: 65
Order:=6; dsolve(x^2*diff(y(x),x$2)+x^3*diff(y(x),x)-(2+x)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \frac {c_{1} x^{3} \left (1+\frac {1}{4} x -\frac {7}{40} x^{2}-\frac {37}{720} x^{3}+\frac {467}{20160} x^{4}+\frac {5647}{806400} x^{5}+\mathrm {O}\left (x^{6}\right )\right )+c_{2} \left (\ln \relax (x ) \left (-x^{3}-\frac {1}{4} x^{4}+\frac {7}{40} x^{5}+\mathrm {O}\left (x^{6}\right )\right )+\left (12-6 x -3 x^{2}+3 x^{3}+\frac {29}{16} x^{4}-\frac {353}{800} x^{5}+\mathrm {O}\left (x^{6}\right )\right )\right )}{x} \]
✓ Solution by Mathematica
Time used: 0.025 (sec). Leaf size: 82
AsymptoticDSolveValue[x^2*y''[x]+x^3*y'[x]-(2+x)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {91 x^4+160 x^3-144 x^2-288 x+576}{576 x}-\frac {1}{48} x^2 (x+4) \log (x)\right )+c_2 \left (\frac {467 x^6}{20160}-\frac {37 x^5}{720}-\frac {7 x^4}{40}+\frac {x^3}{4}+x^2\right ) \]