Internal problem ID [10972]
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: 148.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }+\left (a \,x^{2+n}+b \,x^{2}+c \right ) y^{\prime }+\left (a n \,x^{n +1}+x^{n} a c +b c \right ) y=0} \]
✗ Solution by Maple
dsolve(x^2*diff(y(x),x$2)+(a*x^(n+2)+b*x^2+c)*diff(y(x),x)+(a*n*x^(n+1)+a*c*x^n+b*c)*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+2)+b*x^2+c)*y'[x]+(a*n*x^(n+1)+a*c*x^n+b*c)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
Not solved