61.18.4 problem 32

Internal problem ID [12265]
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 : 32
Date solved : Tuesday, January 28, 2025 at 01:53:08 AM
CAS classification : [_Riccati]

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

✗ Solution by Maple

dsolve(diff(y(x),x)=lambda*arccot(x)^n*y(x)^2-b*lambda*x^m*arccot(x)^n*y(x)+b*m*x^(m-1),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]*ArcCot[x]^n*y[x]^2-b*\[Lambda]*x^m*ArcCot[x]^n*y[x]+b*m*x^(m-1),y[x],x,IncludeSingularSolutions -> True]
 

Not solved