61.13.10 problem 56

Internal problem ID [12230]
Book : Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second edition
Section : Chapter 1, section 1.2. Riccati Equation. subsection 1.2.6-5. Equations containing combinations of trigonometric functions.
Problem number : 56
Date solved : Tuesday, January 28, 2025 at 01:28:48 AM
CAS classification : [_Riccati]

\begin{align*} y^{\prime }&=y^{2}-2 \lambda ^{2} \tan \left (x \right )^{2}-2 \lambda ^{2} \cot \left (\lambda x \right )^{2} \end{align*}

✗ Solution by Maple

dsolve(diff(y(x),x)=y(x)^2-2*lambda^2*tan(x)^2-2*lambda^2*cot(lambda*x)^2,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]^2-2*\[Lambda]^2*Tan[x]^2-2*\[Lambda]^2*Cot[\[Lambda]*x]^2,y[x],x,IncludeSingularSolutions -> True]
 

Not solved