Internal problem ID [9890]
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: 40.
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}-a \,{\mathrm e}^{\lambda x} f \relax (x ) y-{\mathrm e}^{\lambda x} a=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 110
dsolve(diff(y(x),x)=diff(f(x),x)*y(x)^2+a*exp(lambda*x)*f(x)*y(x)+a*exp(lambda*x),y(x), singsol=all)
\[ y \relax (x ) = -\frac {f \relax (x ) {\mathrm e}^{\int \frac {{\mathrm e}^{\lambda x} f \relax (x )^{2} a -2 \frac {d}{d x}f \relax (x )}{f \relax (x )}d x}+\int \left (\frac {d}{d x}f \relax (x )\right ) {\mathrm e}^{a \left (\int {\mathrm e}^{\lambda x} f \relax (x )d x \right )-2 \left (\int \frac {\frac {d}{d x}f \relax (x )}{f \relax (x )}d x \right )}d x +c_{1}}{f \relax (x ) \left (\int \left (\frac {d}{d x}f \relax (x )\right ) {\mathrm e}^{a \left (\int {\mathrm e}^{\lambda x} f \relax (x )d x \right )-2 \left (\int \frac {\frac {d}{d x}f \relax (x )}{f \relax (x )}d x \right )}d x +c_{1}\right )} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y'[x]==f'[x]*y[x]^2+a*Exp[\[Lambda]*x]*f[x]*y[x]+a*Exp[\[Lambda]*x],y[x],x,IncludeSingularSolutions -> True]
Not solved