61.24.14 problem 14

Internal problem ID [12348]
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 : 14
Date solved : Monday, March 31, 2025 at 05:14:05 AM
CAS classification : [[_Abel, `2nd type`, `class A`]]

\begin{align*} y y^{\prime }&=\left (a \left (n -1\right ) x +b \left (2 \lambda +n \right )\right ) x^{\lambda -1} \left (a x +b \right )^{-\lambda -2} y-\left (a n x +b \left (\lambda +n \right )\right ) x^{2 \lambda -1} \left (a x +b \right )^{-2 \lambda -3} \end{align*}

✗ Maple

ode:=y(x)*diff(y(x),x) = (a*(n-1)*x+b*(2*lambda+n))*x^(lambda-1)*(a*x+b)^(-lambda-2)*y(x)-(a*n*x+b*(lambda+n))*x^(2*lambda-1)*(a*x+b)^(-2*lambda-3); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=y[x]*D[y[x],x]==(a*(n-1)*x+b*(2*\[Lambda]+n))*x^(\[Lambda]-1)*(a*x+b)^(-\[Lambda]-2)*y[x]-(a*n*x+b*(\[Lambda]+n))*x^(2*\[Lambda]-1)*(a*x+b)^(-2*\[Lambda]-3); 
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_") 
n = symbols("n") 
y = Function("y") 
ode = Eq(-x**(lambda_ - 1)*(a*x + b)**(-lambda_ - 2)*(a*x*(n - 1) + b*(2*lambda_ + n))*y(x) + x**(2*lambda_ - 1)*(a*x + b)**(-2*lambda_ - 3)*(a*n*x + b*(lambda_ + n)) + y(x)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out