15.16.4 problem 4

Internal problem ID [3224]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 25, page 112
Problem number : 4
Date solved : Monday, January 27, 2025 at 07:26:39 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{2} y^{\prime \prime }+5 x y^{\prime }+10 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 27

dsolve(x^2*diff(y(x),x$2)+5*x*diff(y(x),x)+10*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {c_{1} \sin \left (\ln \left (x \right ) \sqrt {6}\right )+c_2 \cos \left (\ln \left (x \right ) \sqrt {6}\right )}{x^{2}} \]

✓ Solution by Mathematica

Time used: 0.035 (sec). Leaf size: 34

DSolve[x^2*D[y[x],{x,2}]+5*x*D[y[x],x]+10*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_2 \cos \left (\sqrt {6} \log (x)\right )+c_1 \sin \left (\sqrt {6} \log (x)\right )}{x^2} \]