78.12.28 problem 5 (d)

Internal problem ID [18315]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 3. Second order linear equations. Section 17. The Homogeneous Equation with Constant Coefficients. Problems at page 125
Problem number : 5 (d)
Date solved : Tuesday, January 28, 2025 at 11:46:06 AM
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)
 

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

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 20

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

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