Internal problem ID [2251]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
\[ \boxed {x^{2} y^{\prime \prime }+y^{\prime } x +16 y=0} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = c_{1} \sin \left (4 \ln \left (x \right )\right )+c_{2} \cos \left (4 \ln \left (x \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.03 (sec). Leaf size: 22
DSolve[x^2*y''[x]+x*y'[x]+16*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 \cos (4 \log (x))+c_2 \sin (4 \log (x)) \]