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 : Sunday, March 30, 2025 at 01:21:16 PM
CAS classification : [[_Emden, _Fowler]]

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

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

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

\[ y = x^{3} \left (c_1 +c_2 \ln \left (x \right )\right ) \]

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

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

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

✓ Sympy. Time used: 0.155 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) - 5*x*Derivative(y(x), x) + 9*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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