55.22.75 problem 75

Internal problem ID [13616]
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 1.3.1-2. Solvable equations and their solutions
Problem number : 75
Date solved : Wednesday, October 01, 2025 at 07:36:17 PM
CAS classification : [[_Abel, `2nd type`, `class A`]]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

Timed Out