Internal problem ID [11079]
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: 255.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (x^{n}+a \right )^{2} y^{\prime \prime }-b \,x^{n -2} \left (\left (b -1\right ) x^{n}+\left (n -1\right ) a \right ) y=0} \]
✓ Solution by Maple
Time used: 0.391 (sec). Leaf size: 75
dsolve((x^n+a)^2*diff(y(x),x$2)-b*x^(n-2)*( (b-1)*x^n+a*(n-1))*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \left (c_{2} \left (a x +x^{n +1}\right ) \operatorname {hypergeom}\left (\left [1, \frac {n -2 b +1}{n}\right ], \left [1+\frac {1}{n}\right ], -\frac {x^{n}}{a}\right )+\left (\frac {x^{n}+a}{a}\right )^{\frac {2 b}{n}} a c_{1} \right ) \left (x^{n}+a \right )^{-\frac {b}{n}} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[(x^n+a)^2*y''[x]-b*x^(n-2)*( (b-1)*x^n+a*(n-1))*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
Not solved