73.17.17 problem 17

Internal problem ID [15480]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 25. Review exercises for part III. page 447
Problem number : 17
Date solved : Monday, March 31, 2025 at 01:39:04 PM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

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

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

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

\[ y = c_1 \sin \left (3 \ln \left (x \right )\right )+c_2 \cos \left (3 \ln \left (x \right )\right ) \]

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 22

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

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

✓ Sympy. Time used: 0.175 (sec). Leaf size: 19

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

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