Internal problem ID [9900]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
Solve \begin {gather*} \boxed {y^{\prime }-y^{2}+\frac {\lambda ^{2}}{4}-\frac {{\mathrm e}^{2 \lambda x} f \left (\frac {{\mathrm e}^{\lambda x} a +b}{{\mathrm e}^{\lambda x} c +d}\right )}{\left ({\mathrm e}^{\lambda x} c +d \right )^{4}}=0} \end {gather*}
✗ 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: 0.0 (sec). Leaf size: 0
DSolve[y'[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