61.21.10 problem 10

Internal problem ID [12321]
Book : Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second edition
Section : Chapter 1, section 1.2. Riccati Equation. subsection 1.2.9. Some Transformations
Problem number : 10
Date solved : Tuesday, January 28, 2025 at 02:36:38 AM
CAS classification : [_Riccati]

\begin{align*} y^{\prime }&=y^{2}-\lambda ^{2}+\frac {f \left (\tanh \left (\lambda x \right )\right )}{\cosh \left (\lambda x \right )^{4}} \end{align*}

✗ Solution by Maple

dsolve(diff(y(x),x)=y(x)^2-lambda^2+cosh(lambda*x)^(-4)*f(tanh(lambda*x)),y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

DSolve[D[y[x],x]==y[x]^2-\[Lambda]^2+Cosh[\[Lambda]*x]^(-4)*f[Tanh[\[Lambda]*x]],y[x],x,IncludeSingularSolutions -> True]
 

Not solved