61.19.21 problem 21

Internal problem ID [12290]
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 : 21
Date solved : Tuesday, January 28, 2025 at 02:09:57 AM
CAS classification : [_Riccati]

\begin{align*} y^{\prime }&=f \left (x \right ) y^{2}+\lambda x y+a f \left (x \right ) {\mathrm e}^{\lambda x} \end{align*}

✗ Solution by Maple

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

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

DSolve[D[y[x],x]==f[x]*y[x]^2+\[Lambda]*x*y[x]+a*f[x]*Exp[\[Lambda]*x],y[x],x,IncludeSingularSolutions -> True]
 

Not solved