61.2.76 problem 76

Internal problem ID [12082]
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 : 76
Date solved : Tuesday, January 28, 2025 at 12:17:07 AM
CAS classification : [_rational, _Riccati]

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

✗ Solution by Maple

dsolve((a*x^n+b*x^m+c)*diff(y(x),x)=a*x^(n-2)*y(x)^2+b*x^(m-1)*y(x)+c,y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

DSolve[(a*x^n+b*x^m+c)*D[y[x],x]==a*x^(n-2)*y[x]^2+b*x^(m-1)*y[x]+c,y[x],x,IncludeSingularSolutions -> True]
 

Not solved