Internal problem ID [2396]
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 11.2. page
739
Problem number: Problem 9.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {\left (x^{2}-3\right ) y^{\prime \prime }-3 y^{\prime } x -5 y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 34
Order:=6; dsolve((x^2-3)*diff(y(x),x$2)-3*x*diff(y(x),x)-5*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (1-\frac {5}{6} x^{2}+\frac {5}{24} x^{4}\right ) y \relax (0)+\left (x -\frac {4}{9} x^{3}+\frac {8}{135} x^{5}\right ) D\relax (y )\relax (0)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 42
AsymptoticDSolveValue[(x^2-3)*y''[x]-3*x*y'[x]-5*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (\frac {8 x^5}{135}-\frac {4 x^3}{9}+x\right )+c_1 \left (\frac {5 x^4}{24}-\frac {5 x^2}{6}+1\right ) \]