44.1.36 problem 38

Internal problem ID [6911]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Exercises 1.1 at page 12
Problem number : 38
Date solved : Monday, January 27, 2025 at 02:34:47 PM
CAS classification : [[_Emden, _Fowler]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 14

dsolve(4*x^2*diff(y(x),x$2)+y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 24

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

\[ y(x)\to \frac {1}{2} \sqrt {x} (c_2 \log (x)+2 c_1) \]