61.33.1 problem 238

Internal problem ID [12739]
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
Date solved : Tuesday, January 28, 2025 at 04:17:23 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{6} y^{\prime \prime }-x^{5} y^{\prime }+a y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.141 (sec). Leaf size: 35

dsolve(x^6*diff(y(x),x$2)-x^5*diff(y(x),x)+a*y(x)=0,y(x), singsol=all)
 

\[ y = x^{2} \left (c_{1} \sinh \left (\frac {\sqrt {-a}}{2 x^{2}}\right )+c_{2} \cosh \left (\frac {\sqrt {-a}}{2 x^{2}}\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.146 (sec). Leaf size: 58

DSolve[x^6*D[y[x],{x,2}]-x^5*D[y[x],x]+a*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} x^2 e^{-\frac {i \sqrt {a}}{2 x^2}} \left (2 c_1 e^{\frac {i \sqrt {a}}{x^2}}-\frac {i c_2}{\sqrt {a}}\right ) \]