60.2.271 problem 848

Internal problem ID [10845]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 848
Date solved : Sunday, March 30, 2025 at 07:13:34 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(y)]`]]

\begin{align*} y^{\prime }&=\frac {\cosh \left (x \right )}{\sinh \left (x \right )}+\textit {\_F1} \left (y-\ln \left (\sinh \left (x \right )\right )\right ) \end{align*}

✓ Maple. Time used: 0.192 (sec). Leaf size: 22

ode:=diff(y(x),x) = 1/sinh(x)*cosh(x)+_F1(y(x)-ln(sinh(x))); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \ln \left (\sinh \left (x \right )\right )+\operatorname {RootOf}\left (x -\int _{}^{\textit {\_Z}}\frac {1}{\textit {\_F1} \left (\textit {\_a} \right )}d \textit {\_a} +c_1 \right ) \]

✓ Mathematica. Time used: 0.378 (sec). Leaf size: 148

ode=D[y[x],x] == Coth[x] + F1[-Log[Sinh[x]] + y[x]]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\int _1^{y(x)}-\frac {\text {F1}(K[2]-\log (\sinh (x))) \int _1^x\left (\frac {(\coth (K[1])+\text {F1}(K[2]-\log (\sinh (K[1])))) \text {F1}''(K[2]-\log (\sinh (K[1])))}{\text {F1}(K[2]-\log (\sinh (K[1])))^2}-\frac {\text {F1}''(K[2]-\log (\sinh (K[1])))}{\text {F1}(K[2]-\log (\sinh (K[1])))}\right )dK[1]-1}{\text {F1}(K[2]-\log (\sinh (x)))}dK[2]+\int _1^x-\frac {\coth (K[1])+\text {F1}(y(x)-\log (\sinh (K[1])))}{\text {F1}(y(x)-\log (\sinh (K[1])))}dK[1]=c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
F1 = Function("F1") 
ode = Eq(-F1(y(x) - log(sinh(x))) + Derivative(y(x), x) - cosh(x)/sinh(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -F1(y(x) - log(sinh(x))) + Derivative(y(x), x) - 1/tanh(x) cannot be solved by the factorable group method