54.4.27 problem 30

Internal problem ID [8611]
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 : 30
Date solved : Monday, January 27, 2025 at 04:17:25 PM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-9 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 15

dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)-9*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {c_{1} x^{6}+c_{2}}{x^{3}} \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 18

DSolve[x^2*D[y[x],{x,2}]+x*D[y[x],x]-9*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_2 x^6+c_1}{x^3} \]