61.21.2 problem 2

Internal problem ID [12313]
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 : 2
Date solved : Tuesday, January 28, 2025 at 02:34:54 AM
CAS classification : [_Riccati]

\begin{align*} y^{\prime }&=y^{2}+\frac {f \left (\frac {1}{x}\right )}{x^{4}} \end{align*}

✗ Solution by Maple

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

Not solved