Internal problem ID [11072]
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: 248.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{n} y^{\prime \prime }+\left (a \,x^{m +n}+1\right ) y^{\prime }+a \,x^{m} \left (1+x^{n -1} m \right ) y=0} \]
✗ Solution by Maple
dsolve(x^n*diff(y(x),x$2)+(a*x^(n+m)+1)*diff(y(x),x)+a*x^m*(1+m*x^(n-1))*y(x)=0,y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[x^n*y''[x]+(a*x^(n+m)+1)*y'[x]+a*x^m*(1+m*x^(n-1))*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
Not solved