61.32.21 problem 230

Internal problem ID [12731]
Book : Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second edition
Section : Chapter 2, Second-Order Differential Equations. section 2.1.2-7
Problem number : 230
Date solved : Tuesday, January 28, 2025 at 04:17:00 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✗ Solution by Maple

dsolve((x^2+a)^2*diff(y(x),x$2)+b*x^n*(x^2+a)*diff(y(x),x)-(b*x^(n+1)+a)*y(x)=0,y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

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

Not solved