61.21.7 problem 7

Internal problem ID [12318]
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 : 7
Date solved : Tuesday, January 28, 2025 at 02:35:11 AM
CAS classification : [_Riccati]

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

✗ Solution by Maple

dsolve(diff(y(x),x)=y(x)^2+exp(2*lambda*x)*f(exp(lambda*x))-1/4*lambda^2,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+Exp[2*\[Lambda]*x]*f[Exp[\[Lambda]*x]]-1/4*\[Lambda]^2,y[x],x,IncludeSingularSolutions -> True]
 

Not solved