74.1.47 problem 54

Internal problem ID [15827]
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 : Tuesday, January 28, 2025 at 08:08:21 AM
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*}

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 14

dsolve([x^2*diff(y(x),x$2)+3*x*diff(y(x),x)+5*y(x)=0,y(1) = 0, D(y)(1) = 1],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 15

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

\[ y(x)\to \frac {\sin (\log (x)) \cos (\log (x))}{x} \]