61.27.49 problem 59

Internal problem ID [12559]
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 : 59
Date solved : Tuesday, January 28, 2025 at 03:21:37 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✗ Solution by Maple

dsolve(diff(y(x),x$2)+(a*x^n+b*x^m)*diff(y(x),x)+(a*b*x^(n+m)+b*(m+1)*x^(m-1)-a*x^(n-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+b*x^m)*D[y[x],x]+(a*b*x^(n+m)+b*(m+1)*x^(m-1)-a*x^(n-1))*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved