61.33.7 problem 245

Internal problem ID [12745]
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 : 245
Date solved : Tuesday, January 28, 2025 at 08:23:59 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{n} y^{\prime \prime }+\left (2 x^{n -1}+a \,x^{2}+b x \right ) y^{\prime }+b y&=0 \end{align*}

✓ Solution by Maple

Time used: 1.456 (sec). Leaf size: 76

dsolve(x^n*diff(y(x),x$2)+(2*x^(n-1)+a*x^2+b*x)*diff(y(x),x)+b*y(x)=0,y(x), singsol=all)
 

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

✗ Solution by Mathematica

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

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

Not solved