73.13.17 problem 20.1 (q)

Internal problem ID [15395]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 20. Euler equations. Additional exercises page 382
Problem number : 20.1 (q)
Date solved : Tuesday, January 28, 2025 at 07:54:20 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} 4 x^{2} y^{\prime \prime }+8 x y^{\prime }+5 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 19

dsolve(4*x^2*diff(y(x),x$2)+8*x*diff(y(x),x)+5*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 24

DSolve[4*x^2*D[y[x],{x,2}]+8*x*D[y[x],x]+5*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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