Internal problem ID [5853]
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: 23.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {9 x^{2} y^{\prime \prime }+9 y^{\prime } x^{2}+2 y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 55
Order:=8; dsolve(9*x^2*diff(y(x),x$2)+9*x^2*diff(y(x),x)+2*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = c_{1} x^{\frac {1}{3}} \left (1-\frac {1}{2} x +\frac {1}{5} x^{2}-\frac {7}{120} x^{3}+\frac {7}{528} x^{4}-\frac {13}{5280} x^{5}+\frac {13}{33660} x^{6}-\frac {247}{4712400} x^{7}+\mathrm {O}\left (x^{8}\right )\right )+c_{2} x^{\frac {2}{3}} \left (1-\frac {1}{2} x +\frac {5}{28} x^{2}-\frac {1}{21} x^{3}+\frac {11}{1092} x^{4}-\frac {11}{6240} x^{5}+\frac {187}{711360} x^{6}-\frac {17}{497952} x^{7}+\mathrm {O}\left (x^{8}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 118
AsymptoticDSolveValue[9*x^2*y''[x]+9*x^2*y'[x]+2*y[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_2 \sqrt [3]{x} \left (-\frac {247 x^7}{4712400}+\frac {13 x^6}{33660}-\frac {13 x^5}{5280}+\frac {7 x^4}{528}-\frac {7 x^3}{120}+\frac {x^2}{5}-\frac {x}{2}+1\right )+c_1 x^{2/3} \left (-\frac {17 x^7}{497952}+\frac {187 x^6}{711360}-\frac {11 x^5}{6240}+\frac {11 x^4}{1092}-\frac {x^3}{21}+\frac {5 x^2}{28}-\frac {x}{2}+1\right ) \]