Internal problem ID [6183]
Book: Elementary differential equations. Rainville, Bedient, Bedient. Prentice Hall. NJ. 8th edition.
1997.
Section: CHAPTER 18. Power series solutions. 18.4 Indicial Equation with Difference of Roots
Nonintegral. Exercises page 365
Problem number: 21.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {9 x^{2} y^{\prime \prime }+2 y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.021 (sec). Leaf size: 27
Order:=8; dsolve(9*x^2*diff(y(x),x$2)+2*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = x^{\frac {1}{3}} \left (c_{2} x^{\frac {1}{3}}+c_{1}\right )+O\left (x^{8}\right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 20
AsymptoticDSolveValue[9*x^2*y''[x]+2*y[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_1 x^{2/3}+c_2 \sqrt [3]{x} \]