61.28.49 problem 109

Internal problem ID [12609]
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
Problem number : 109
Date solved : Tuesday, January 28, 2025 at 03:23:03 AM
CAS classification : [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

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

✓ Solution by Maple

Time used: 0.003 (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)
 

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

✗ Solution by Mathematica

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

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

Not solved