68.1.47 problem 54

Internal problem ID [17114]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 1. Introduction to Differential Equations. Exercises 1.1, page 10
Problem number : 54
Date solved : Thursday, October 02, 2025 at 01:43:22 PM
CAS classification : [[_Emden, _Fowler]]

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

With initial conditions

\begin{align*} y \left (1\right )&=0 \\ y^{\prime }\left (1\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.059 (sec). Leaf size: 14

ode:=x^2*diff(diff(y(x),x),x)+3*x*diff(y(x),x)+5*y(x) = 0; 
ic:=[y(1) = 0, D(y)(1) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {\sin \left (2 \ln \left (x \right )\right )}{2 x} \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 15

ode=x^2*D[y[x],{x,2}]+3*x*D[y[x],x]+5*y[x]==0; 
ic={y[1]==0,Derivative[1][y][1]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {\sin (\log (x)) \cos (\log (x))}{x} \end{align*}

✓ Sympy. Time used: 0.123 (sec). Leaf size: 12

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 = {y(1): 0, Subs(Derivative(y(x), x), x, 1): 1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {\sin {\left (2 \log {\left (x \right )} \right )}}{2 x} \]