54.4.30 problem 33

Internal problem ID [8614]
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 : 33
Date solved : Monday, January 27, 2025 at 04:17:29 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{2} y^{\prime \prime }+5 x y^{\prime }+5 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 19

dsolve(x^2*diff(y(x),x$2)+5*x*diff(y(x),x)+5*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {c_{1} \sin \left (\ln \left (x \right )\right )+c_{2} \cos \left (\ln \left (x \right )\right )}{x^{2}} \]

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 22

DSolve[x^2*D[y[x],{x,2}]+5*x*D[y[x],x]+5*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_2 \cos (\log (x))+c_1 \sin (\log (x))}{x^2} \]