5.13 problem 13

Internal problem ID [10461]

Book: Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second edition
Section: Chapter 1, section 1.2. Riccati Equation. subsection 1.2.4-1. Equations with hyperbolic sine and cosine
Problem number: 13.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_Riccati]

\[ \boxed {y^{\prime }-y^{2}=-\lambda ^{2}+a \cosh \left (\lambda x \right )^{n} \sinh \left (\lambda x \right )^{-n -4}} \]

✗ Solution by Maple

dsolve(diff(y(x),x)=y(x)^2-lambda^2+a*cosh(lambda*x)^n*sinh(lambda*x)^(-n-4),y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

DSolve[y'[x]==y[x]^2-\[Lambda]^2+a*Cosh[\[Lambda]*x]^n*Sinh[\[Lambda]*x]^(-n-4),y[x],x,IncludeSingularSolutions -> True]
                                                                                    
                                                                                    
 

Not solved