61.7.5 problem 5

Internal problem ID [12156]
Book : Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second edition
Section : Chapter 1, section 1.2. Riccati Equation. subsection 1.2.5-1. Equations Containing Logarithmic Functions
Problem number : 5
Date solved : Tuesday, January 28, 2025 at 12:45:32 AM
CAS classification : [_Riccati]

\begin{align*} x y^{\prime }&=x y^{2}-a^{2} x \ln \left (\beta x \right )^{2 k}+a k \ln \left (\beta x \right )^{k -1} \end{align*}

✗ Solution by Maple

dsolve(x*diff(y(x),x)=x*y(x)^2-a^2*x*(ln(beta*x))^(2*k)+a*k*(ln(beta*x))^(k-1),y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

DSolve[x*D[y[x],x]==x*y[x]^2-a^2*x*(Log[\[Beta]*x])^(2*k)+a*k*(Log[\[Beta]*x])^(k-1),y[x],x,IncludeSingularSolutions -> True]
 

Not solved