Internal problem ID [6187]
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: 27.
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*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 15
dsolve(9*x^2*diff(y(x),x$2)+2*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} x^{\frac {2}{3}}+c_{2} x^{\frac {1}{3}} \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 22
DSolve[9*x^2*y''[x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt [3]{x} \left (c_2 \sqrt [3]{x}+c_1\right ) \\ \end{align*}