54.4.29 problem 32

Internal problem ID [8613]
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 : 32
Date solved : Monday, January 27, 2025 at 04:17:27 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 14

dsolve(x^2*diff(y(x),x$2)-5*x*diff(y(x),x)+9*y(x)=0,y(x), singsol=all)
 

\[ y = x^{3} \left (c_{2} \ln \left (x \right )+c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 18

DSolve[x^2*D[y[x],{x,2}]-5*x*D[y[x],x]+9*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^3 (3 c_2 \log (x)+c_1) \]