Internal problem ID [2253]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {x^{2} y^{\prime \prime }+5 y^{\prime } x +10 y=0} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = \frac {c_{1} \sin \left (\sqrt {6}\, \ln \left (x \right )\right )+c_{2} \cos \left (\sqrt {6}\, \ln \left (x \right )\right )}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.044 (sec). Leaf size: 34
DSolve[x^2*y''[x]+5*x*y'[x]+10*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {c_2 \cos \left (\sqrt {6} \log (x)\right )+c_1 \sin \left (\sqrt {6} \log (x)\right )}{x^2} \]