61.11.8 problem 34

Internal problem ID [12208]
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
Date solved : Tuesday, January 28, 2025 at 01:07:58 AM
CAS classification : [_Riccati]

\begin{align*} y^{\prime }&=a \tan \left (\lambda x \right )^{n} y^{2}-a \,b^{2} \tan \left (\lambda x \right )^{n +2}+b \lambda \tan \left (\lambda x \right )^{2}+b \lambda \end{align*}

✗ 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: 0.000 (sec). Leaf size: 0

DSolve[D[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],x,IncludeSingularSolutions -> True]
 

Not solved