Internal problem ID [10640]
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: 37.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, `_with_symmetry_[F(x),G(x)]`], _Riccati]
\[ \boxed {y^{\prime }-g \left (x \right ) \left (y-f \left (x \right )\right )^{2}=f^{\prime }\left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(diff(y(x),x)=g(x)*(y(x)-f(x))^2+diff(f(x),x),y(x), singsol=all)
\[ y \left (x \right ) = f \left (x \right )+\frac {1}{c_{1} -\left (\int g \left (x \right )d x \right )} \]
✓ Solution by Mathematica
Time used: 0.35 (sec). Leaf size: 31
DSolve[y'[x]==g[x]*(y[x]-f[x])^2+f'[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to f(x)+\frac {1}{-\int _1^xg(K[2])dK[2]+c_1} y(x)\to f(x) \end{align*}