61.21.8 problem 8

Internal problem ID [12319]
Book : Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second edition
Section : Chapter 1, section 1.2. Riccati Equation. subsection 1.2.9. Some Transformations
Problem number : 8
Date solved : Tuesday, January 28, 2025 at 02:35:15 AM
CAS classification : [_Riccati]

\begin{align*} y^{\prime }&=y^{2}-\frac {\lambda ^{2}}{4}+\frac {{\mathrm e}^{2 \lambda x} f \left (\frac {a \,{\mathrm e}^{\lambda x}+b}{c \,{\mathrm e}^{\lambda x}+d}\right )}{\left (c \,{\mathrm e}^{\lambda x}+d \right )^{4}} \end{align*}

✗ Solution by Maple

dsolve(diff(y(x),x)=y(x)^2-lambda^2/4+exp(2*lambda*x)/(c*exp(lambda*x)+d)^4*f((a*exp(lambda*x)+b)/(c*exp(lambda*x)+d)),y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[D[y[x],x]==y[x]^2-\[Lambda]^2/4+Exp[2*\[Lambda]*x]/(c*Exp[\[Lambda]*x]+d)^4*f[(a*Exp[\[Lambda]*x]+b)/(c*Exp[\[Lambda]*x]+d)],y[x],x,IncludeSingularSolutions -> True]
 

Not solved