61.16.6 problem 24

Internal problem ID [12257]
Book : Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second edition
Section : Chapter 1, section 1.2. Riccati Equation. subsection 1.2.7-3. Equations containing arctangent.
Problem number : 24
Date solved : Tuesday, January 28, 2025 at 01:46:56 AM
CAS classification : [_Riccati]

\begin{align*} y^{\prime }&=\lambda \arctan \left (x \right )^{n} y^{2}+\beta m \,x^{m -1}-\lambda \,\beta ^{2} x^{2 m} \arctan \left (x \right )^{n} \end{align*}

✗ Solution by Maple

dsolve(diff(y(x),x)=lambda*arctan(x)^n*y(x)^2+beta*m*x^(m-1)-lambda*beta^2*x^(2*m)*arctan(x)^n,y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

DSolve[D[y[x],x]==\[Lambda]*ArcTan[x]^n*y[x]^2+\[Beta]*m*x^(m-1)-\[Lambda]*\[Beta]^2*x^(2*m)*ArcTan[x]^n,y[x],x,IncludeSingularSolutions -> True]
 

Not solved