Internal problem ID [9869]
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: 19.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
Solve \begin {gather*} \boxed {y^{\prime }-y^{2} f \relax (x )+a \,{\mathrm e}^{\lambda x} g \relax (x ) y-a \lambda \,{\mathrm e}^{\lambda x}-a^{2} {\mathrm e}^{2 \lambda x} \left (g \relax (x )-f \relax (x )\right )=0} \end {gather*}
✗ Solution by Maple
dsolve(diff(y(x),x)=f(x)*y(x)^2-a*exp(lambda*x)*g(x)*y(x)+a*lambda*exp(lambda*x)+a^2*exp(2*lambda*x)*(g(x)-f(x)),y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y'[x]==f[x]*y[x]^2-a*Exp[\[Lambda]*x]*g[x]*y[x]+a*\[Lambda]*Exp[\[Lambda]*x]+a^2*Exp[2*\[Lambda]*x]*(g[x]-f[x]),y[x],x,IncludeSingularSolutions -> True]
Not solved