9.3 problem 3

Internal problem ID [10501]

Book: Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second edition
Section: Chapter 1, section 1.2. Riccati Equation. subsection 1.2.6-1. Equations with sine
Problem number: 3.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_Riccati]

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

✗ Solution by Maple

dsolve(diff(y(x),x)=y(x)^2+lambda^2+c*sin(lambda*x+a)^n*sin(lambda*x+b)^(-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+c*Sin[\[Lambda]*x+a]^n*Sin[\[Lambda]*x+b]^(-n-4),y[x],x,IncludeSingularSolutions -> True]
                                                                                    
                                                                                    
 

Not solved