Internal problem ID [10947]
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: 123.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {x^{2} y^{\prime \prime }+a x y^{\prime }+y b=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 52
dsolve(x^2*diff(y(x),x$2)+a*x*diff(y(x),x)+b*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = x^{-\frac {a}{2}} \sqrt {x}\, \left (x^{\frac {\sqrt {a^{2}-2 a -4 b +1}}{2}} c_{1} +x^{-\frac {\sqrt {a^{2}-2 a -4 b +1}}{2}} c_{2} \right ) \]
✓ Solution by Mathematica
Time used: 0.069 (sec). Leaf size: 57
DSolve[x^2*y''[x]+a*x*y'[x]+b*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x^{\frac {1}{2} \left (-\sqrt {a^2-2 a-4 b+1}-a+1\right )} \left (c_2 x^{\sqrt {a^2-2 a-4 b+1}}+c_1\right ) \]