54.2.209 problem 786

Internal problem ID [12083]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 786
Date solved : Wednesday, October 01, 2025 at 12:13:25 AM
CAS classification : [[_homogeneous, `class D`], _Riccati]

\begin{align*} y^{\prime }&=\frac {y \ln \left (x \right )+\cosh \left (x \right ) x a y^{2}+\cosh \left (x \right ) x^{3} b}{x \ln \left (x \right )} \end{align*}

✓ Maple. Time used: 0.019 (sec). Leaf size: 33

ode:=diff(y(x),x) = (y(x)*ln(x)+cosh(x)*x*a*y(x)^2+cosh(x)*x^3*b)/x/ln(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\tan \left (\sqrt {b a}\, \left (\int \frac {x \cosh \left (x \right )}{\ln \left (x \right )}d x +c_1 \right )\right ) x \sqrt {b a}}{a} \]

✓ Mathematica. Time used: 0.147 (sec). Leaf size: 47

ode=D[y[x],x] == (b*x^3*Cosh[x] + Log[x]*y[x] + a*x*Cosh[x]*y[x]^2)/(x*Log[x]); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {1}{a K[1]^2+b}dK[1]=\int _1^x\frac {\cosh (K[2]) K[2]}{\log (K[2])}dK[2]+c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
b = symbols("b") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - (a*x*y(x)**2*cosh(x) + b*x**3*cosh(x) + y(x)*log(x))/(x*log(x)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out