19.32 problem 32

Internal problem ID [10625]

Book: Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second edition
Section: Chapter 1, section 1.2. Riccati Equation. subsection 1.2.8-1. Equations containing arbitrary functions (but not containing their derivatives).
Problem number: 32.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_Riccati]

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

✗ Solution by Maple

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

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

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

Not solved