Internal problem ID [4855]
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. 6.3.1 page
250
Problem number: 20.
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 y^{\prime }+\left (x^{6}-36\right ) y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.024 (sec). Leaf size: 27
Order:=6; dsolve(9*x^2*diff(y(x),x$2)+9*x*diff(y(x),x)+(x^6-36)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (1+\mathrm {O}\left (x^{6}\right )\right ) c_{1} x^{2}+\frac {c_{2} \left (-144+\mathrm {O}\left (x^{6}\right )\right )}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 16
AsymptoticDSolveValue[9*x^2*y''[x]+9*x*y'[x]+(x^6-36)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 x^2+\frac {c_1}{x^2} \]