73.13.10 problem 20.1 (j)

Internal problem ID [15388]
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 (j)
Date solved : Tuesday, January 28, 2025 at 07:54:08 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{2} y^{\prime \prime }-x y^{\prime }+10 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 21

dsolve(x^2*diff(y(x),x$2)-x*diff(y(x),x)+10*y(x)=0,y(x), singsol=all)
 

\[ y = x \left (c_{1} \sin \left (3 \ln \left (x \right )\right )+c_{2} \cos \left (3 \ln \left (x \right )\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.026 (sec). Leaf size: 24

DSolve[x^2*D[y[x],{x,2}]-x*D[y[x],x]+10*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x (c_2 \cos (3 \log (x))+c_1 \sin (3 \log (x))) \]