Internal problem ID [14802]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.9, page 215
Problem number: 1.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {x^{2} y^{\prime \prime }+6 y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 41
Order:=6; dsolve(x^2*diff(y(x),x$2)+6*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \sqrt {x}\, \left (c_{1} x^{-\frac {i \sqrt {23}}{2}}+c_{2} x^{\frac {i \sqrt {23}}{2}}\right )+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 44
AsymptoticDSolveValue[x^2*y''[x]+6*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 x^{\frac {1}{2} \left (1+i \sqrt {23}\right )}+c_2 x^{\frac {1}{2} \left (1-i \sqrt {23}\right )} \]