61.2.9 problem 9

Internal problem ID [12015]
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 : 9
Date solved : Monday, January 27, 2025 at 11:49:13 PM
CAS classification : [_Riccati]

\begin{align*} y^{\prime }&=y^{2}+k \left (a x +b \right )^{n} \left (c x +d \right )^{-n -4} \end{align*}

✗ Solution by Maple

dsolve(diff(y(x),x)=y(x)^2+k*(a*x+b)^n*(c*x+d)^(-n-4),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+k*(a*x+b)^n*(c*x+d)^(-n-4),y[x],x,IncludeSingularSolutions -> True]
 

Not solved