Internal problem ID [9886]
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]
Solve \begin {gather*} \boxed {y^{\prime }+f^{\prime }\relax (x ) y^{2}-f \relax (x ) g \relax (x ) y+g \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (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)
\[ y \relax (x ) = \frac {f \relax (x ) {\mathrm e}^{\int \frac {f \relax (x )^{2} g \relax (x )-2 \frac {d}{d x}f \relax (x )}{f \relax (x )}d x}+\int \left (\frac {d}{d x}f \relax (x )\right ) {\mathrm e}^{\int f \relax (x ) g \relax (x )d x -2 \left (\int \frac {\frac {d}{d x}f \relax (x )}{f \relax (x )}d x \right )}d x -c_{1}}{f \relax (x ) \left (\int \left (\frac {d}{d x}f \relax (x )\right ) {\mathrm e}^{\int f \relax (x ) g \relax (x )d x -2 \left (\int \frac {\frac {d}{d x}f \relax (x )}{f \relax (x )}d x \right )}d x -c_{1}\right )} \]
✗ 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