61.33.23 problem 261

Internal problem ID [12761]
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 : 261
Date solved : Tuesday, January 28, 2025 at 04:18:19 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 13.873 (sec). Leaf size: 68

dsolve((a*x^n+b*x^m+c)*diff(y(x),x$2)+(lambda-x)*diff(y(x),x)+y(x)=0,y(x), singsol=all)
 

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

✗ Solution by Mathematica

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

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

Not solved