50.9.28 problem 5(d)

Internal problem ID [7964]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 2. Second-Order Linear Equations. Section 2.1. Linear Equations with Constant Coefficients. Page 62
Problem number : 5(d)
Date solved : Monday, January 27, 2025 at 03:34:14 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} 4 x^{2} y^{\prime \prime }-3 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 15

dsolve(4*x^2*diff(y(x),x$2)-3*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {c_{1} x^{2}+c_{2}}{\sqrt {x}} \]

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 20

DSolve[4*x^2*D[y[x],{x,2}]-3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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