61.9.5 problem 5

Internal problem ID [12179]
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 : 5
Date solved : Tuesday, January 28, 2025 at 12:51:34 AM
CAS classification : [_Riccati]

\begin{align*} y^{\prime }&=y^{2}+a \sin \left (b x \right )^{m} y+a \sin \left (b x \right )^{m} \end{align*}

✗ Solution by Maple

dsolve(diff(y(x),x)=y(x)^2+a*sin(b*x)^m*y(x)+a*sin(b*x)^m,y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[D[y[x],x]==y[x]^2+a*Sin[b*x]^m*y[x]+a*Sin[b*x]^m,y[x],x,IncludeSingularSolutions -> True]
 

Not solved