Internal problem ID [2250]
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: 1.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {x^{2} y^{\prime \prime }-4 y^{\prime } x +y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(x^2*diff(y(x),x$2)-4*x*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = x^{\frac {5}{2}} \left (x^{\frac {\sqrt {21}}{2}} c_{1} +x^{-\frac {\sqrt {21}}{2}} c_{2} \right ) \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 34
DSolve[x^2*y''[x]-4*x*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x^{\frac {5}{2}-\frac {\sqrt {21}}{2}} \left (c_2 x^{\sqrt {21}}+c_1\right ) \]