Internal problem ID [11082]
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: 258.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (a \,x^{n}+b \right )^{2} y^{\prime \prime }+c \,x^{m} \left (a \,x^{n}+b \right ) y^{\prime }+\left (c \,x^{m}-a n \,x^{n -1}-1\right ) y=0} \]
✗ Solution by Maple
dsolve((a*x^n+b)^2*diff(y(x),x$2)+c*x^m*(a*x^n+b)*diff(y(x),x)+(c*x^m-a*n*x^(n-1)-1)*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+b)^2*y''[x]+c*x^m*(a*x^n+b)*y'[x]+(c*x^m-a*n*x^(n-1)-1)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
Not solved