Internal problem ID [2252]
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: 3.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {4 x^{2} y^{\prime \prime }-16 y^{\prime } x +25 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(4*x^2*diff(y(x),x$2)-16*x*diff(y(x),x)+25*y(x)=0,y(x), singsol=all)
\[ y = c_{1} x^{\frac {5}{2}}+c_{2} x^{\frac {5}{2}} \ln \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 25
DSolve[4*x^2*y''[x]-16*x*y'[x]+25*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} x^{5/2} (5 c_2 \log (x)+2 c_1) \]