Internal problem ID [10928]
Book: Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev.
Second edition
Section: Chapter 2, Second-Order Differential Equations. section 2.1.2-3 Equation of form
\((a x + b)y''+f(x)y'+g(x)y=0\)
Problem number: 104.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x y^{\prime \prime }+\left (x^{m +n} a b +x^{n} n a +b \,x^{m}+1-2 n \right ) y^{\prime }+a^{2} b n \,x^{2 n +m -1} y=0} \]
✗ Solution by Maple
dsolve(x*diff(y(x),x$2)+(a*b*x^(n+m)+a*n*x^n+b*x^m+1-2*n)*diff(y(x),x)+a^2*b*n*x^(2*n+m-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*y''[x]+(a*b*x^(n+m)+a*n*x^n+b*x^m+1-2*n)*y'[x]+a^2*b*n*x^(2*n+m-1)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
Not solved