Internal problem ID [10620]
Book: Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev.
Second edition
Section: Chapter 1, section 1.2. Riccati Equation. subsection 1.2.8-1. Equations containing
arbitrary functions (but not containing their derivatives).
Problem number: 27.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
\[ \boxed {y^{\prime }-y^{2} f \left (x \right )+a x \ln \left (x \right ) f \left (x \right ) y=a \ln \left (x \right )+a} \]
✗ Solution by Maple
dsolve(diff(y(x),x)=f(x)*y(x)^2-a*x*ln(x)*f(x)*y(x)+a*ln(x)+a,y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y'[x]==f[x]*y[x]^2-a*x*Log[x]*f[x]*y[x]+a*Log[x]+a,y[x],x,IncludeSingularSolutions -> True]
Not solved