13.10 problem 56

Internal problem ID [10554]

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.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_Riccati]

\[ \boxed {y^{\prime }-y^{2}=-2 \lambda ^{2} \cot \left (\lambda x \right )^{2}-2 \lambda ^{2} \tan \left (x \right )^{2}} \]

✗ 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: 0.0 (sec). Leaf size: 0

DSolve[y'[x]==y[x]^2-2*\[Lambda]^2*Tan[x]^2-2*\[Lambda]^2*Cot[\[Lambda]*x]^2,y[x],x,IncludeSingularSolutions -> True]
                                                                                    
                                                                                    
 

Not solved