85.65.3 problem 4 (b)

Internal problem ID [22883]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 4. Linear differential equations. B Exercises at page 213
Problem number : 4 (b)
Date solved : Thursday, October 02, 2025 at 09:16:12 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{2} y^{\prime \prime }-x y^{\prime }+4 y&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 25

ode:=x^2*diff(diff(y(x),x),x)-x*diff(y(x),x)+4*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 32

ode=x^2*D[y[x],{x,2}]-x*D[y[x],{x,1}]+4*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to x \left (c_1 \cos \left (\sqrt {3} \log (x)\right )+c_2 \sin \left (\sqrt {3} \log (x)\right )\right ) \end{align*}

✓ Sympy. Time used: 0.108 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) - x*Derivative(y(x), x) + 4*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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