Internal problem ID [9736]
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: 4.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
Solve \begin {gather*} \boxed {y^{\prime } x -y^{2} x +a^{2} x \ln \left (\beta x \right )^{2}-a=0} \end {gather*}
✗ Solution by Maple
dsolve(x*diff(y(x),x)=x*y(x)^2-a^2*x*(ln(beta*x))^2+a,y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[x*y'[x]==x*y[x]^2-a^2*x*(Log[\[Beta]*x])^2+a,y[x],x,IncludeSingularSolutions -> True]
Not solved