61.2.29 problem 29

Internal problem ID [12035]
Book : Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second edition
Section : Chapter 1, section 1.2. Riccati Equation. 1.2.2. Equations Containing Power Functions
Problem number : 29
Date solved : Monday, January 27, 2025 at 11:52:35 PM
CAS classification : [_Riccati]

\begin{align*} y^{\prime }&=-\left (n +1\right ) x^{n} y^{2}+a \,x^{n +m +1}-a \,x^{m} \end{align*}

✗ Solution by Maple

dsolve(diff(y(x),x)=-(n+1)*x^n*y(x)^2+a*x^(n+m+1)-a*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]==-(n+1)*x^n*y[x]^2+a*x^(n+m+1)-a*x^m,y[x],x,IncludeSingularSolutions -> True]
 

Not solved