19.20 problem 20

Internal problem ID [10613]

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: 20.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_Riccati]

\[ \boxed {y^{\prime }-y^{2} f \left (x \right )=2 a \lambda x \,{\mathrm e}^{\lambda \,x^{2}}-a^{2} f \left (x \right ) {\mathrm e}^{2 \lambda \,x^{2}}} \]

✗ Solution by Maple

dsolve(diff(y(x),x)=f(x)*y(x)^2+2*a*lambda*x*exp(lambda*x^2)-a^2*f(x)*exp(2*lambda*x^2),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+2*a*\[Lambda]*x*Exp[\[Lambda]*x^2]-a^2*f[x]*Exp[2*\[Lambda]*x^2],y[x],x,IncludeSingularSolutions -> True]
                                                                                    
                                                                                    
 

Not solved