35.7.13 problem 16 (d)

Internal problem ID [6195]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 7. Other second-Order equations. page 435
Problem number : 16 (d)
Date solved : Monday, January 27, 2025 at 01:47:21 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{2} y^{\prime \prime }-x y^{\prime }+6 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 25

dsolve(x^2*diff(y(x),x$2)-x*diff(y(x),x)+6*y(x)=0,y(x), singsol=all)
 

\[ y = x \left (c_{1} \sin \left (\sqrt {5}\, \ln \left (x \right )\right )+c_{2} \cos \left (\sqrt {5}\, \ln \left (x \right )\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.033 (sec). Leaf size: 32

DSolve[x^2*D[y[x],{x,2}]-x*D[y[x],x]+6*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x \left (c_2 \cos \left (\sqrt {5} \log (x)\right )+c_1 \sin \left (\sqrt {5} \log (x)\right )\right ) \]