Internal problem ID [6156]
Book: Elementary differential equations. Rainville, Bedient, Bedient. Prentice Hall. NJ. 8th edition.
1997.
Section: CHAPTER 17. Power series solutions. 17.5. Solutions Near an Ordinary Point. Exercises page
355
Problem number: 21.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, _with_symmetry_[0,F(x)]]]
Solve \begin {gather*} \boxed {\left (x^{2}+4\right ) y^{\prime \prime }+x y^{\prime }-9 y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 34
Order:=8; dsolve((x^2+4)*diff(y(x),x$2)+x*diff(y(x),x)-9*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (1+\frac {9}{8} x^{2}+\frac {15}{128} x^{4}-\frac {7}{1024} x^{6}\right ) y \relax (0)+\left (\frac {1}{3} x^{3}+x \right ) D\relax (y )\relax (0)+O\left (x^{8}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 42
AsymptoticDSolveValue[(x^2+4)*y''[x]+x*y'[x]-9*y[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_2 \left (\frac {x^3}{3}+x\right )+c_1 \left (-\frac {7 x^6}{1024}+\frac {15 x^4}{128}+\frac {9 x^2}{8}+1\right ) \]