15.16.2 problem 2

Internal problem ID [3222]
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 : 2
Date solved : Monday, January 27, 2025 at 07:26:35 AM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+16 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 19

dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)+16*y(x)=0,y(x), singsol=all)
 

\[ y = c_{1} \sin \left (4 \ln \left (x \right )\right )+c_2 \cos \left (4 \ln \left (x \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 22

DSolve[x^2*D[y[x],{x,2}]+x*D[y[x],x]+16*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 \cos (4 \log (x))+c_2 \sin (4 \log (x)) \]