61.20.2 problem 35

Internal problem ID [12304]
Book : Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second edition
Section : Chapter 1, section 1.2. Riccati Equation. subsection 1.2.8-2. Equations containing arbitrary functions and their derivatives.
Problem number : 35
Date solved : Tuesday, January 28, 2025 at 02:34:33 AM
CAS classification : [_Riccati]

\begin{align*} y^{\prime }&=f \left (x \right ) y^{2}-f \left (x \right ) g \left (x \right ) y+g^{\prime }\left (x \right ) \end{align*}

✗ Solution by Maple

dsolve(diff(y(x),x)=f(x)*y(x)^2-f(x)*g(x)*y(x)+diff(g(x),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-f[x]*g[x]*y[x]+D[ g[x],x],y[x],x,IncludeSingularSolutions -> True]
 

Not solved