61.19.23 problem 23

Internal problem ID [12292]
Book : Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second edition
Section : Chapter 1, section 1.2. Riccati Equation. subsection 1.2.8-1. Equations containing arbitrary functions (but not containing their derivatives).
Problem number : 23
Date solved : Tuesday, January 28, 2025 at 02:14:56 AM
CAS classification : [_Riccati]

\begin{align*} y^{\prime }&=f \left (x \right ) y^{2}-a \coth \left (\lambda x \right )^{2} \left (a f \left (x \right )+\lambda \right )+a \lambda \end{align*}

✗ Solution by Maple

dsolve(diff(y(x),x)=f(x)*y(x)^2-a*coth(lambda*x)^2*(a*f(x)+lambda)+a*lambda,y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

DSolve[D[y[x],x]==f[x]*y[x]^2-a*Coth[\[Lambda]*x]^2*(a*f[x]+\[Lambda])+a*\[Lambda],y[x],x,IncludeSingularSolutions -> True]
 

Not solved