11.8 problem 34

Internal problem ID [10532]

Book: Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second edition
Section: Chapter 1, section 1.2. Riccati Equation. subsection 1.2.6-3. Equations with tangent.
Problem number: 34.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_Riccati]

\[ \boxed {y^{\prime }-a \tan \left (\lambda x \right )^{n} y^{2}=-a \,b^{2} \tan \left (\lambda x \right )^{2+n}+b \lambda \tan \left (\lambda x \right )^{2}+b \lambda } \]

✗ Solution by Maple

dsolve(diff(y(x),x)=a*tan(lambda*x)^n*y(x)^2-a*b^2*tan(lambda*x)^(n+2)+b*lambda*tan(lambda*x)^2+b*lambda,y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.0 (sec). Leaf size: 0

DSolve[y'[x]==a*Tan[\[Lambda]*x]^n*y[x]^2-a*b^2*Tan[\[Lambda]*x]^(n+2)+b*\[Lambda]*Tan[\[Lambda]*x]^2+b*\[Lambda],y[x],x,IncludeSingularSolutions -> True]
                                                                                    
                                                                                    
 

Not solved