61.21.3 problem 3

Internal problem ID [12314]
Book : Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second edition
Section : Chapter 1, section 1.2. Riccati Equation. subsection 1.2.9. Some Transformations
Problem number : 3
Date solved : Tuesday, January 28, 2025 at 02:34:56 AM
CAS classification : [_Riccati]

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

✗ Solution by Maple

dsolve(diff(y(x),x)=y(x)^2+1/(c*x+d)^4*f((a*x+b)/(c*x+d)),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+1/(c*x+d)^4*f[(a*x+b)/(c*x+d)],y[x],x,IncludeSingularSolutions -> True]
 

Not solved