Internal problem ID [4777]
Book: Notes on Diffy Qs. Differential Equations for Engineers. By by Jiri Lebl, 2013.
Section: Chapter 7. POWER SERIES METHODS. 7.3.2 The method of Frobenius. Exercises. page
300
Problem number: 7.3.102.
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: 0.022 (sec). Leaf size: 39
Order:=6; dsolve(x^2*diff(y(x),x$2)-y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = x^{\frac {1}{2}-\frac {\sqrt {5}}{2}} c_{1}+x^{\frac {1}{2}+\frac {\sqrt {5}}{2}} c_{2}+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 38
AsymptoticDSolveValue[x^2*y''[x]-y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 x^{\frac {1}{2} \left (1+\sqrt {5}\right )}+c_2 x^{\frac {1}{2} \left (1-\sqrt {5}\right )} \]