20.1.19 problem Problem 25

Internal problem ID [3576]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.2, Basic Ideas and Terminology. page 21
Problem number : Problem 25
Date solved : Tuesday, March 04, 2025 at 04:52:13 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{2} y^{\prime \prime }+5 x y^{\prime }+4 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)+4*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 18

ode=x^2*D[y[x],{x,2}]+5*x*D[y[x],x]+4*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {2 c_2 \log (x)+c_1}{x^2} \]

✓ Sympy. Time used: 0.152 (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) + 4*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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