Internal problem ID [11084]
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: 260.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (a \,x^{n +1}+b \,x^{n}+c \right )^{2} y^{\prime \prime }+\left (\alpha \,x^{n}+\beta \,x^{n -1}+\gamma \right ) y^{\prime }+\left (n \left (-a n -a +\alpha \right ) x^{n -1}+\left (n -1\right ) \left (-n b +\beta \right ) x^{n -2}\right ) y=0} \]
✗ Solution by Maple
dsolve((a*x^(n+1)+b*x^n+c)^2*diff(y(x),x$2)+(alpha*x^n+beta*x^(n-1)+gamma)*diff(y(x),x)+(n*(alpha-a-a*n)*x^(n-1)+(n-1)*(beta-b*n)*x^(n-2))*y(x)=0,y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[(a*x^(n+1)+b*x^n+c)^2*y''[x]+(\[Alpha]*x^n+\[Beta]*x^(n-1)+\[Gamma])*y'[x]+(n*(\[Alpha]-a-a*n)*x^(n-1)+(n-1)*(\[Beta]-b*n)*x^(n-2))*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
Not solved