61.3.7 problem 7

Internal problem ID [12091]
Book : Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second edition
Section : Chapter 1, section 1.2. Riccati Equation. subsection 1.2.3. Equations Containing Exponential Functions
Problem number : 7
Date solved : Tuesday, January 28, 2025 at 12:21:45 AM
CAS classification : [_Riccati]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 1436

dsolve(diff(y(x),x)=y(x)^2+a*exp(2*lambda*x)*(exp(lambda*x)+b)^n-1/4*lambda^2,y(x), singsol=all)
 

\[ \text {Expression too large to display} \]

✗ Solution by Mathematica

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

DSolve[D[y[x],x]==y[x]^2+a*Exp[2*\[Lambda]*x]*(Exp[\[Lambda]*x]+b)^n-1/4*\[Lambda]^2,y[x],x,IncludeSingularSolutions -> True]
 

Not solved