Internal problem ID [11087]
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: 263.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {2 \left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime \prime }+a n \,x^{n -1} b m \,x^{m -1} y^{\prime }+y d=0} \]
✗ Solution by Maple
dsolve(2*(a*x^n+b*x^m+c)*diff(y(x),x$2)+(a*n*x^(n-1)*b*m*x^(m-1))*diff(y(x),x)+d*y(x)=0,y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[2*(a*x^n+b*x^m+c)*y''[x]+(a*n*x^(n-1)*b*m*x^(m-1))*y'[x]+d*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
Not solved