14.6 problem 6

Internal problem ID [10563]

Book: Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second edition
Section: Chapter 1, section 1.2. Riccati Equation. subsection 1.2.7-1. Equations containing arcsine.
Problem number: 6.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_Riccati]

\[ \boxed {y^{\prime }-\lambda \arcsin \left (x \right )^{n} y^{2}=\beta m \,x^{m -1}-\lambda \,\beta ^{2} x^{2 m} \arcsin \left (x \right )^{n}} \]

✗ Solution by Maple

dsolve(diff(y(x),x)=lambda*arcsin(x)^n*y(x)^2+beta*m*x^(m-1)-lambda*beta^2*x^(2*m)*arcsin(x)^n,y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

DSolve[y'[x]==\[Lambda]*ArcSin[x]^n*y[x]^2+\[Beta]*m*x^(m-1)-\[Lambda]*\[Beta]^2*x^(2*m)*ArcSin[x]^n,y[x],x,IncludeSingularSolutions -> True]
                                                                                    
                                                                                    
 

Not solved