61.24.76 problem 76

Internal problem ID [12410]
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 : 76
Date solved : Monday, March 31, 2025 at 05:32:15 AM
CAS classification : [[_Abel, `2nd type`, `class A`]]

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

✗ Maple

ode:=y(x)*diff(y(x),x) = (a*sinh(x)+b)*y(x)-a*b*cosh(x)+c; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=y[x]*D[y[x],x]==(a*Sinh[x]+b)*y[x]-a*b*Cosh[x]+c; 
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") 
y = Function("y") 
ode = Eq(a*b*cosh(x) - c - (a*sinh(x) + b)*y(x) + y(x)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out