73.13.13 problem 20.1 (m)

Internal problem ID [15391]
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 (m)
Date solved : Tuesday, January 28, 2025 at 07:54:15 AM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

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

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

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