Internal problem ID [10639]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
\[ \boxed {x^{2} y^{\prime }-x^{4} f \left (x \right ) y^{2}=1} \]
✗ 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: 0.0 (sec). Leaf size: 0
DSolve[x^2*y'[x]==x^4*f[x]*y[x]^2+1,y[x],x,IncludeSingularSolutions -> True]
Not solved