Internal problem ID [11073]
Book: Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev.
Second edition
Section: Chapter 2, Second-Order Differential Equations. section 2.1.2-8. Other equations.
Problem number: 238.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {x^{6} y^{\prime \prime }-y^{\prime } x^{5}+a y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 37
dsolve(x^6*diff(y(x),x$2)-x^5*diff(y(x),x)+a*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} x^{2} \sinh \left (\frac {\sqrt {-a}}{2 x^{2}}\right )+c_{2} x^{2} \cosh \left (\frac {\sqrt {-a}}{2 x^{2}}\right ) \]
✓ Solution by Mathematica
Time used: 0.239 (sec). Leaf size: 58
DSolve[x^6*y''[x]-x^5*y'[x]+a*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} x^2 e^{-\frac {i \sqrt {a}}{2 x^2}} \left (2 c_1 e^{\frac {i \sqrt {a}}{x^2}}-\frac {i c_2}{\sqrt {a}}\right ) \]