Internal problem ID [10933]
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: 109.
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)]`]]
\[ \boxed {\left (x +\gamma \right ) y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime }+\left (a n \,x^{n -1}+x^{m -1} b m \right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 63
dsolve((x+gamma)*diff(y(x),x$2)+(a*x^n+b*x^m+c)*diff(y(x),x)+(a*n*x^(n-1)+b*m*x^(m-1))*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \left (c_{1} \left (\int \frac {{\mathrm e}^{\int \frac {a \,x^{n}+b \,x^{m}+c -1}{x +\gamma }d x}}{x +\gamma }d x \right )+c_{2} \right ) {\mathrm e}^{-\left (\int \frac {a \,x^{n}+b \,x^{m}+c -1}{x +\gamma }d x \right )} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[(x+\[Gamma])*y''[x]+(a*x^n+b*x^m+c)*y'[x]+(a*n*x^(n-1)+b*m*x^(m-1))*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
Not solved