Internal problem ID [10629]
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: 36.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
\[ \boxed {y^{\prime }+f^{\prime }\left (x \right ) y^{2}-f \left (x \right ) g \left (x \right ) y=-g \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 102
dsolve(diff(y(x),x)=-diff(f(x),x)*y(x)^2+f(x)*g(x)*y(x)-g(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {f \left (x \right ) {\mathrm e}^{\int \frac {g \left (x \right ) f \left (x \right )^{2}-2 \frac {d}{d x}f \left (x \right )}{f \left (x \right )}d x}+\int \left (\frac {d}{d x}f \left (x \right )\right ) {\mathrm e}^{\int g \left (x \right ) f \left (x \right )d x -2 \left (\int \frac {\frac {d}{d x}f \left (x \right )}{f \left (x \right )}d x \right )}d x -c_{1}}{f \left (x \right ) \left (\int \left (\frac {d}{d x}f \left (x \right )\right ) {\mathrm e}^{\int g \left (x \right ) f \left (x \right )d x -2 \left (\int \frac {\frac {d}{d x}f \left (x \right )}{f \left (x \right )}d x \right )}d x -c_{1} \right )} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y'[x]==-f'[x]*y[x]^2+f[x]*g[x]*y[x]-g[x],y[x],x,IncludeSingularSolutions -> True]
Not solved