55.26.24 problem 24

Internal problem ID [13771]
Book : Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second edition
Section : Chapter 1, section 1.4. Equations Containing Polynomial Functions of y. subsection 1.4.1-2 Abel equations of the first kind.
Problem number : 24
Date solved : Thursday, October 02, 2025 at 08:06:25 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _Abel]

\begin{align*} y^{\prime }&=a \,{\mathrm e}^{2 \lambda x} y^{3}+b \,{\mathrm e}^{\lambda x} y^{2}+c y+d \,{\mathrm e}^{-\lambda x} \end{align*}

✓ Maple. Time used: 0.020 (sec). Leaf size: 40

ode:=diff(y(x),x) = a*exp(2*lambda*x)*y(x)^3+b*exp(lambda*x)*y(x)^2+c*y(x)+d*exp(-lambda*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \operatorname {RootOf}\left (-x +\int _{}^{\textit {\_Z}}\frac {1}{\textit {\_a}^{3} a +\textit {\_a}^{2} b +\textit {\_a} c +\lambda \textit {\_a} +d}d \textit {\_a} +c_1 \right ) {\mathrm e}^{-\lambda x} \]

✓ Mathematica. Time used: 101.384 (sec). Leaf size: 5390

ode=D[y[x],x]==a*Exp[2*\[Lambda]*x]*y[x]^3+b*Exp[ \[Lambda] *x]*y[x]^2+c*y[x]+d*Exp[- \[Lambda] *x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Too large to display

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
b = symbols("b") 
d = symbols("d") 
c = symbols("c") 
lambda_ = symbols("lambda_") 
y = Function("y") 
ode = Eq(-a*y(x)**3*exp(2*lambda_*x) - b*y(x)**2*exp(lambda_*x) - c*y(x) - d*exp(-lambda_*x) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out