61.21.4 problem 4

Internal problem ID [12315]
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 : 4
Date solved : Tuesday, January 28, 2025 at 02:35:00 AM
CAS classification : [_Riccati]

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

✗ Solution by Maple

dsolve(x^2*diff(y(x),x)=x^4*f(x)*y(x)^2+1,y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

DSolve[x^2*D[y[x],x]==x^4*f[x]*y[x]^2+1,y[x],x,IncludeSingularSolutions -> True]
 

Not solved