61.27.38 problem 48

Internal problem ID [12548]
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
Problem number : 48
Date solved : Tuesday, January 28, 2025 at 03:21:17 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✗ Solution by Maple

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

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

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

Not solved