Internal problem ID [10924]
Book: Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev.
Second edition
Section: Chapter 2, Second-Order Differential Equations. section 2.1.2-3 Equation of form
\((a x + b)y''+f(x)y'+g(x)y=0\)
Problem number: 100.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x y^{\prime \prime }+\left (a \,x^{n}+b \,x^{n -1}+2\right ) y^{\prime }+y x^{n -2} b=0} \]
✓ Solution by Maple
Time used: 0.344 (sec). Leaf size: 53
dsolve(x*diff(y(x),x$2)+(a*x^n+b*x^(n-1)+2)*diff(y(x),x)+(b*x^(n-2))*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (a x +b \right ) \left (c_{2} \left (\int \frac {{\mathrm e}^{-\frac {\left (a x \left (n -1\right )+b n \right ) x^{n -1}}{n \left (n -1\right )}}}{\left (a x +b \right )^{2}}d x \right )+c_{1} \right )}{x} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[x*y''[x]+(a*x^n+b*x^(n-1)+2)*y'[x]+(b*x^(n-2))*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
Not solved