Internal problem ID [10944]
Book: Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev.
Second edition
Section: Chapter 2, Second-Order Differential Equations. section 2.1.2-4 Equation of form
\(x^2 y''+f(x)y'+g(x)y=0\)
Problem number: 110.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {x^{2} y^{\prime \prime }+a y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 35
dsolve(x^2*diff(y(x),x$2)+a*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} x^{\frac {1}{2}+\frac {\sqrt {1-4 a}}{2}}+c_{2} x^{\frac {1}{2}-\frac {\sqrt {1-4 a}}{2}} \]
✓ Solution by Mathematica
Time used: 0.057 (sec). Leaf size: 42
DSolve[x^2*y''[x]+a*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x^{\frac {1}{2}-\frac {1}{2} \sqrt {1-4 a}} \left (c_2 x^{\sqrt {1-4 a}}+c_1\right ) \]