55.23.8 problem 8

Internal problem ID [13625]
Book : Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second edition
Section : Chapter 1, section 1.3. Abel Equations of the Second Kind. subsection 1.3.2.
Problem number : 8
Date solved : Wednesday, October 01, 2025 at 07:43:21 PM
CAS classification : [[_Abel, `2nd type`, `class A`]]

\begin{align*} y y^{\prime }&=\left (a \,{\mathrm e}^{\lambda x}+b \,{\mathrm e}^{-\lambda x}\right ) y+1 \end{align*}

✗ Maple

ode:=y(x)*diff(y(x),x) = (exp(lambda*x)*a+b*exp(-lambda*x))*y(x)+1; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=y[x]*D[y[x],x]==(a*Exp[\[Lambda]*x]+b*Exp[-\[Lambda]*x])*y[x]+1; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
b = symbols("b") 
lambda_ = symbols("lambda_") 
y = Function("y") 
ode = Eq((-a*exp(lambda_*x) - b*exp(-lambda_*x))*y(x) + y(x)*Derivative(y(x), x) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out