61.11.8 problem 34

Internal problem ID [12129]
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 : Sunday, March 30, 2025 at 11:01:27 PM
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*}

✗ Maple

ode:=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; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=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]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
b = symbols("b") 
lambda_ = symbols("lambda_") 
n = symbols("n") 
y = Function("y") 
ode = Eq(a*b**2*tan(lambda_*x)**(n + 2) - a*y(x)**2*tan(lambda_*x)**n - b*lambda_*tan(lambda_*x)**2 - b*lambda_ + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out