19.25 problem 25

Internal problem ID [10618]

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: 25.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_Riccati]

\[ \boxed {y^{\prime } x -y^{2} f \left (x \right )=a -a^{2} f \left (x \right ) \ln \left (x \right )^{2}} \]

✗ Solution by Maple

dsolve(x*diff(y(x),x)=f(x)*y(x)^2+a-a^2*f(x)*(ln(x))^2,y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.0 (sec). Leaf size: 0

DSolve[x*y'[x]==f[x]*y[x]^2+a-a^2*f[x]*(Log[x])^2,y[x],x,IncludeSingularSolutions -> True]
                                                                                    
                                                                                    
 

Not solved