Internal problem ID [6940]
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]]
\[ \boxed {9 x^{2} y^{\prime \prime }+2 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve(9*x^2*diff(y(x),x$2)+2*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = x^{\frac {1}{3}} \left (c_{1} x^{\frac {1}{3}}+c_{2} \right ) \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 22
DSolve[9*x^2*y''[x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \sqrt [3]{x} \left (c_2 \sqrt [3]{x}+c_1\right ) \]