Internal problem ID [10876]
Book: Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev.
Second edition
Section: Chapter 2, Second-Order Differential Equations. section 2.1.2-2 Equation of form
\(y''+f(x)y'+g(x)y=0\)
Problem number: 52.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+\left (a b \,x^{n}+b \,x^{n -1}+2 a \right ) y^{\prime }+a^{2} \left (b \,x^{n}+1\right ) y=0} \]
✗ Solution by Maple
dsolve(diff(y(x),x$2)+(a*b*x^n+b*x^(n-1)+2*a)*diff(y(x),x)+a^2*(b*x^n+1)*y(x)=0,y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y''[x]+(a*b*x^n+b*x^(n-1)+2*a)*y'[x]+a^2*(b*x^n+1)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
Not solved