Internal problem ID [5833]
Book: DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL,
WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th
edition.
Section: CHAPTER 6 SERIES SOLUTIONS OF LINEAR EQUATIONS. 6.3 SOLUTIONS ABOUT
SINGULAR POINTS. EXERCISES 6.3. Page 255
Problem number: 3.
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 )^{2} y^{\prime \prime }+\left (x +3\right ) y^{\prime }+2 y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 74
Order:=8; dsolve((x^2-9)^2*diff(y(x),x$2)+(x+3)*diff(y(x),x)+2*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (1-\frac {1}{81} x^{2}+\frac {1}{6561} x^{3}-\frac {289}{708588} x^{4}+\frac {304}{23914845} x^{5}-\frac {194981}{7748409780} x^{6}+\frac {1732937}{1464449448420} x^{7}\right ) y \relax (0)+\left (x -\frac {1}{54} x^{2}-\frac {13}{2187} x^{3}-\frac {131}{236196} x^{4}-\frac {596}{1594323} x^{5}-\frac {78469}{2582803260} x^{6}-\frac {13738871}{488149816140} x^{7}\right ) D\relax (y )\relax (0)+O\left (x^{8}\right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 98
AsymptoticDSolveValue[(x^2-9)^2*y''[x]+(x+3)*y'[x]+2*y[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_1 \left (\frac {1732937 x^7}{1464449448420}-\frac {194981 x^6}{7748409780}+\frac {304 x^5}{23914845}-\frac {289 x^4}{708588}+\frac {x^3}{6561}-\frac {x^2}{81}+1\right )+c_2 \left (-\frac {13738871 x^7}{488149816140}-\frac {78469 x^6}{2582803260}-\frac {596 x^5}{1594323}-\frac {131 x^4}{236196}-\frac {13 x^3}{2187}-\frac {x^2}{54}+x\right ) \]