61.33.17 problem 255

Internal problem ID [12755]
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
Date solved : Tuesday, January 28, 2025 at 08:24:16 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (x^{n}+a \right )^{2} y^{\prime \prime }-b \,x^{n -2} \left (\left (b -1\right ) x^{n}+a \left (n -1\right )\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 1.258 (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)
 

\[ y = \left (x^{n}+a \right )^{-\frac {b}{n}} \left (c_{2} \left (a x +x^{n +1}\right ) \operatorname {hypergeom}\left (\left [1, \frac {n -2 b +1}{n}\right ], \left [1+\frac {1}{n}\right ], -\frac {x^{n}}{a}\right )+\left (\frac {x^{n}+a}{a}\right )^{\frac {2 b}{n}} a c_{1} \right ) \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[(x^n+a)^2*D[y[x],{x,2}]-b*x^(n-2)*( (b-1)*x^n+a*(n-1))*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved