Internal problem ID [4825]
Book: A FIRST COURSE IN DIFFERENTIAL EQUATIONS with Modeling Applications. Dennis G.
Zill. 9th edition. Brooks/Cole. CA, USA.
Section: Chapter 6. SERIES SOLUTIONS OF LINEAR EQUATIONS. Exercises. 6.2 page
239
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 x^{2} y^{\prime }+2 y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.017 (sec). Leaf size: 47
Order:=6; 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);
\[ y \relax (x ) = c_{1} x^{\frac {1}{3}} \left (1-\frac {1}{2} x +\frac {1}{5} x^{2}-\frac {7}{120} x^{3}+\frac {7}{528} x^{4}-\frac {13}{5280} x^{5}+\mathrm {O}\left (x^{6}\right )\right )+c_{2} x^{\frac {2}{3}} \left (1-\frac {1}{2} x +\frac {5}{28} x^{2}-\frac {1}{21} x^{3}+\frac {11}{1092} x^{4}-\frac {11}{6240} x^{5}+\mathrm {O}\left (x^{6}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 90
AsymptoticDSolveValue[9*x^2*y''[x]+9*x^2*y'[x]+2*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \sqrt [3]{x} \left (-\frac {13 x^5}{5280}+\frac {7 x^4}{528}-\frac {7 x^3}{120}+\frac {x^2}{5}-\frac {x}{2}+1\right )+c_1 x^{2/3} \left (-\frac {11 x^5}{6240}+\frac {11 x^4}{1092}-\frac {x^3}{21}+\frac {5 x^2}{28}-\frac {x}{2}+1\right ) \]