Internal problem ID [6192]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 17
dsolve(x^2*diff(y(x),x$2)-5*x*diff(y(x),x)+9*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = x^{3} c_{1}+c_{2} x^{3} \ln \relax (x ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 18
DSolve[x^2*y''[x]-5*x*y'[x]+9*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x^3 (3 c_2 \log (x)+c_1) \\ \end{align*}