Internal problem ID [6144]
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: 9.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (x^{2}-9\right ) y^{\prime \prime }+3 x y^{\prime }-3 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: 29
Order:=8; dsolve((x^2-9)*diff(y(x),x$2)+3*x*diff(y(x),x)-3*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (1-\frac {1}{6} x^{2}-\frac {5}{648} x^{4}-\frac {7}{11664} x^{6}\right ) y \relax (0)+D\relax (y )\relax (0) x +O\left (x^{8}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 34
AsymptoticDSolveValue[(x^2-9)*y''[x]+3*x*y'[x]-3*y[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_1 \left (-\frac {7 x^6}{11664}-\frac {5 x^4}{648}-\frac {x^2}{6}+1\right )+c_2 x \]