61.29.34 problem 143

Internal problem ID [12643]
Book : Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second edition
Section : Chapter 2, Second-Order Differential Equations. section 2.1.2-4
Problem number : 143
Date solved : Tuesday, January 28, 2025 at 03:24:10 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✗ Solution by Maple

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

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

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

Not solved