61.33.12 problem 250

Internal problem ID [12750]
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 : 250
Date solved : Tuesday, January 28, 2025 at 04:17:42 AM
CAS classification : [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 33

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

\[ y = \left (\left (\int \frac {1}{\left (a \,x^{n}+b x +c \right )^{2}}d x \right ) c_{1} +c_{2} \right ) \left (a \,x^{n}+b x +c \right ) \]

✗ Solution by Mathematica

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

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

Not solved