Internal problem ID [6521]
Book: Own collection of miscellaneous problems
Section: section 4.0
Problem number: 50.
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 (x^{2}-8\right ) y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.03 (sec). Leaf size: 35
Order:=6; dsolve(x^2*diff(y(x), x$2)-x*diff(y(x), x)+(x^2-8)*y(x) = 0,y(x),type='series',x=0);
\[ y \relax (x ) = c_{1} x^{4} \left (1-\frac {1}{16} x^{2}+\frac {1}{640} x^{4}+\mathrm {O}\left (x^{6}\right )\right )+\frac {c_{2} \left (-86400-10800 x^{2}-1350 x^{4}+\mathrm {O}\left (x^{6}\right )\right )}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 42
AsymptoticDSolveValue[x^2*y''[x]-x*y'[x]+(x^2-8)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {x^2}{64}+\frac {1}{x^2}+\frac {1}{8}\right )+c_2 \left (\frac {x^8}{640}-\frac {x^6}{16}+x^4\right ) \]