Internal problem ID [10968]
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: 144.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }+a \,x^{n} y^{\prime }+\left (a b \,x^{n +2 m}-b^{2} x^{4 m +2}+a m \,x^{n -1}-m^{2}-m \right ) y=0} \]
✗ Solution by Maple
dsolve(x^2*diff(y(x),x$2)+a*x^n*diff(y(x),x)+(a*b*x^(n+2*m)-b^2*x^(4*m+2)+a*m*x^(n-1)-m^2-m)*y(x)=0,y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[x^2*y''[x]+a*x^n*y'[x]+(a*b*x^(n+2*m)-b^2*x^(4*m+2)+a*m*x^(n-1)-m^2-m)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
Not solved