61.33.25 problem 263

Internal problem ID [12763]
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 : 263
Date solved : Tuesday, January 28, 2025 at 04:18:22 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✗ Solution by Maple

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

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

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

Not solved