Internal problem ID [11081]
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: 257.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (x^{n}+a \right )^{2} y^{\prime \prime }+b \,x^{m} \left (x^{n}+a \right ) y^{\prime }-x^{n -2} \left (b \,x^{m +1}+a n -a \right ) y=0} \]
✗ Solution by Maple
dsolve((x^n+a)^2*diff(y(x),x$2)+b*x^m*(x^n+a)*diff(y(x),x)-x^(n-2)*(b*x^(m+1)+a*n-a)*y(x)=0,y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[(x^n+a)^2*y''[x]+b*x^m*(x^n+a)*y'[x]-x^(n-2)*(b*x^(m+1)+a*n-a)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
Not solved