61.31.20 problem 201

Internal problem ID [12701]
Book : Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second edition
Section : Chapter 2, Second-Order Differential Equations. section 2.1.2-6
Problem number : 201
Date solved : Tuesday, January 28, 2025 at 08:11:21 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (a \,x^{3}+x^{2}+b \right ) y^{\prime \prime }+a^{2} x \left (x^{2}-b \right ) y^{\prime }-a^{3} b x y&=0 \end{align*}

✓ Solution by Maple

Time used: 1.873 (sec). Leaf size: 79

dsolve((a*x^3+x^2+b)*diff(y(x),x$2)+a^2*x*(x^2-b)*diff(y(x),x)-a^3*b*x*y(x)=0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{-a x} \left (c_{2} \left (\int {\mathrm e}^{a \left (\int \frac {x^{4} a^{2}+2 a \,x^{3}+\left (a^{2} b +2\right ) x^{2}+4 a x b +2 b}{\left (a \,x^{3}+x^{2}+b \right ) \left (a x +2\right )}d x \right )}d x \right )+c_{1} \right ) \left (a x +2\right ) \]

✗ Solution by Mathematica

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

DSolve[(a*x^3+x^2+b)*D[y[x],{x,2}]+a^2*x*(x^2-b)*D[y[x],x]-a^3*b*x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

Timed out