19.24 problem 24

Internal problem ID [10617]

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: 24.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_Riccati]

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

✗ Solution by Maple

dsolve(diff(y(x),x)=f(x)*y(x)^2-a^2*f(x)+a*lambda*sinh(lambda*x)-a^2*f(x)*sinh(lambda*x)^2,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^2*f[x]+a*\[Lambda]*Sinh[\[Lambda]*x]-a^2*f[x]*Sinh[\[Lambda]*x]^2,y[x],x,IncludeSingularSolutions -> True]
                                                                                    
                                                                                    
 

Not solved