Internal problem ID [11074]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
\[ \boxed {\left (a \,x^{n}+b x +c \right ) y^{\prime \prime }-a n \left (n -1\right ) x^{n -2} y=0} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = \left (\left (\int \frac {1}{\left (a \,x^{n}+b x +c \right )^{2}}d x \right ) c_{1} +c_{2} \right ) \left (a \,x^{n}+b x +c \right ) \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[(a*x^n+b*x+c)*y''[x]==a*n*(n-1)*x^(n-2)*y[x],y[x],x,IncludeSingularSolutions -> True]
Not solved