Internal problem ID [11066]
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: 242.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{n} y^{\prime \prime }+a x y^{\prime }-\left (b^{2} x^{n}+2 b \,x^{n -1}+a b x +a \right ) y=0} \]
✗ Solution by Maple
dsolve(x^n*diff(y(x),x$2)+a*x*diff(y(x),x)-(b^2*x^n+2*b*x^(n-1)+a*b*x+a)*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*y'[x]-(b^2*x^n+2*b*x^(n-1)+a*b*x+a)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
Not solved