Internal problem ID [4847]
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: 10.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }+x y^{\prime }+\left (2 x^{2}-64\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: 35
Order:=6; dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)+(2*x^2-64)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = c_{1} x^{8} \left (1-\frac {1}{18} x^{2}+\frac {1}{720} x^{4}+\mathrm {O}\left (x^{6}\right )\right )+\frac {c_{2} \left (-27360196043587190784000000-1954299717399085056000000 x^{2}-81429154891628544000000 x^{4}+\mathrm {O}\left (x^{6}\right )\right )}{x^{8}} \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 46
AsymptoticDSolveValue[x^2*y''[x]+x*y'[x]+(2*x^2-64)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (\frac {x^{12}}{720}-\frac {x^{10}}{18}+x^8\right )+c_1 \left (\frac {1}{x^8}+\frac {1}{14 x^6}+\frac {1}{336 x^4}\right ) \]