61.24.68 problem 68

Internal problem ID [12402]
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 1.3.3-2.
Problem number : 68
Date solved : Monday, March 31, 2025 at 05:30:07 AM
CAS classification : [[_Abel, `2nd type`, `class A`]]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

Timed Out