Internal problem ID [9789]
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]
Solve \begin {gather*} \boxed {y^{\prime }-a \left (\tan ^{n}\left (\lambda x \right )\right ) y^{2}+a \,b^{2} \left (\tan ^{n +2}\left (\lambda x \right )\right )-b \lambda \left (\tan ^{2}\left (\lambda x \right )\right )-b \lambda =0} \end {gather*}
✗ 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