61.18.8 problem 36

Internal problem ID [12269]
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 : 36
Date solved : Tuesday, January 28, 2025 at 01:57:59 AM
CAS classification : [_Riccati]

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

✗ Solution by Maple

dsolve(x*diff(y(x),x)=(a*x^(2*m)*y(x)^2+b*x^n*y(x)+c)*arccot(x)^m-n*y(x),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]==(a*x^(2*m)*y[x]^2+b*x^n*y[x]+c)*ArcCot[x]^m-n*y[x],y[x],x,IncludeSingularSolutions -> True]
 

Not solved