Internal problem ID [6502]
Book: Own collection of miscellaneous problems
Section: section 4.0
Problem number: 31.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }+y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.027 (sec). Leaf size: 41
Order:=6; dsolve(x^2*diff(y(x), x$2) +y(x) = 0,y(x),type='series',x=0);
\[ y \relax (x ) = x^{\frac {1}{2}-\frac {i \sqrt {3}}{2}} c_{1}+x^{\frac {1}{2}+\frac {i \sqrt {3}}{2}} c_{2}+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 26
AsymptoticDSolveValue[x^2*y''[x] +y[x] == 0,y[x],{x,0,5}]
\[ y(x)\to c_1 x^{-(-1)^{2/3}}+c_2 x^{\sqrt [3]{-1}} \]