61.33.5 problem 243

Internal problem ID [12743]
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 : 243
Date solved : Tuesday, January 28, 2025 at 04:17:29 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 1.205 (sec). Leaf size: 56

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

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

✗ Solution by Mathematica

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

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

Not solved