73.13.23 problem 20.2 (e)

Internal problem ID [15401]
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 : 20.2 (e)
Date solved : Tuesday, January 28, 2025 at 07:54:33 AM
CAS classification : [[_Emden, _Fowler]]

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

With initial conditions

\begin{align*} y \left (1\right )&=3\\ y^{\prime }\left (1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.027 (sec). Leaf size: 16

dsolve([x^2*diff(y(x),x$2)-x*diff(y(x),x)+2*y(x)=0,y(1) = 3, D(y)(1) = 0],y(x), singsol=all)
 

\[ y = -3 x \left (-\cos \left (\ln \left (x \right )\right )+\sin \left (\ln \left (x \right )\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 17

DSolve[{x^2*D[y[x],{x,2}]-x*D[y[x],x]+2*y[x]==0,{y[1]==3,Derivative[1][y][1]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 3 x (\cos (\log (x))-\sin (\log (x))) \]