61.23.9 problem 9

Internal problem ID [12331]
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 : 9
Date solved : Monday, March 31, 2025 at 05:10:43 AM
CAS classification : [[_Abel, `2nd type`, `class A`]]

\begin{align*} y y^{\prime }&=a y \cosh \left (x \right )+1 \end{align*}

✗ Maple

ode:=y(x)*diff(y(x),x) = a*y(x)*cosh(x)+1; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=y[x]*D[y[x],x]==a*y[x]*Cosh[x]+1; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

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

NotImplementedError : The given ODE -a*cosh(x) + Derivative(y(x), x) - 1/y(x) cannot be solved by the factorable group method