78.9.12 problem 7

Internal problem ID [18181]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 3. Second order linear equations. Section 14. Introduction. Problems at page 112
Problem number : 7
Date solved : Thursday, March 13, 2025 at 11:48:27 AM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} x^{2} y^{\prime \prime }-3 x y^{\prime }-5 y&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 15

ode:=x^2*diff(diff(y(x),x),x)-3*x*diff(y(x),x)-5*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 18

ode=x^2*D[y[x],{x,2}] -3*x*D[y[x],x]-5*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.148 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) - 3*x*Derivative(y(x), x) - 5*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1}}{x} + C_{2} x^{5} \]