61.33.24 problem 262

Internal problem ID [12762]
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 : 262
Date solved : Tuesday, January 28, 2025 at 08:24:22 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime \prime }+\left (\lambda ^{2}-x^{2}\right ) y^{\prime }+\left (x +\lambda \right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 3.186 (sec). Leaf size: 76

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

\[ y = -\left (\left (\int {\mathrm e}^{\int \frac {\lambda ^{3}-x \,\lambda ^{2}-\lambda \,x^{2}+x^{3}-2 x^{m} b -2 a \,x^{n}-2 c}{\left (a \,x^{n}+x^{m} b +c \right ) \left (-\lambda +x \right )}d x}d x \right ) c_{1} +c_{2} \right ) \left (\lambda -x \right ) \]

✗ 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]^2-x^2)*D[y[x],x]+(x+\[Lambda])*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved