Internal problem ID [10915]
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: 91.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x y^{\prime \prime }+a \,x^{n} y^{\prime }+\left (a b \,x^{n}-a \,x^{n -1}-b^{2} x +2 b \right ) y=0} \]
✗ Solution by Maple
dsolve(x*diff(y(x),x$2)+a*x^n*diff(y(x),x)+(a*b*x^n-a*x^(n-1)-b^2*x+2*b)*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*x^n*y'[x]+(a*b*x^n-a*x^(n-1)-b^2*x+2*b)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
Not solved